Daily Papers

Neural audio codecs have made significant strides in efficiently mapping raw audio waveforms into discrete token representations, which are foundational for contemporary audio generative models. However, most existing codecs are optimized primarily for reconstruction quality, often at the expense of the downstream modelability of the encoded tokens. Motivated by the need to overcome this bottleneck, we introduce MagiCodec, a novel single-layer, streaming Transformer-based audio codec. MagiCodec is designed with a multistage training pipeline that incorporates Gaussian noise injection and latent regularization, explicitly targeting the enhancement of semantic expressiveness in the generated codes while preserving high reconstruction fidelity. We analytically derive the effect of noise injection in the frequency domain, demonstrating its efficacy in attenuating high-frequency components and fostering robust tokenization. Extensive experimental evaluations show that MagiCodec surpasses state-of-the-art codecs in both reconstruction quality and downstream tasks. Notably, the tokens produced by MagiCodec exhibit Zipf-like distributions, as observed in natural languages, thereby improving compatibility with language-model-based generative architectures. The code and pre-trained models are available at https://github.com/Ereboas/MagiCodec.

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We first derive two hierarchical bounds on the generalization error in terms of the Kullback-Leibler (KL) divergence or the 1-Wasserstein distance between the train and test distributions of the network internal representations. The KL divergence bound shrinks as the layer index increases, while the Wasserstein bound implies the existence of a layer that serves as a generalization funnel, which attains a minimal 1-Wasserstein distance. Analytic expressions for both bounds are derived under the setting of binary Gaussian classification with linear DNNs. To quantify the contraction of the relevant information measures when moving deeper into the network, we analyze the strong data processing inequality (SDPI) coefficient between consecutive layers of three regularized DNN models: Dropout, DropConnect, and Gaussian noise injection. This enables refining our generalization bounds to capture the contraction as a function of the network architecture parameters. Specializing our results to DNNs with a finite parameter space and the Gibbs algorithm reveals that deeper yet narrower network architectures generalize better in those examples, although how broadly this statement applies remains a question.

Machine learning (ML) models frequently rely on training data that may include sensitive or personal information, raising substantial privacy concerns. Legislative frameworks such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA) have necessitated the development of strategies that preserve privacy while maintaining the utility of data. In this paper, we investigate the capability of Large Language Models (LLMs) to generate synthetic datasets integrated with Differential Privacy (DP) mechanisms, thereby enabling data-driven research and model training without direct exposure of sensitive information. Our approach incorporates DP-based noise injection methods, including Laplace and Gaussian distributions, into the data generation process. We then evaluate the utility of these DP-enhanced synthetic datasets by comparing the performance of ML models trained on them against models trained on the original data. To substantiate privacy guarantees, we assess the resilience of the generated synthetic data to membership inference attacks and related threats. The experimental results demonstrate that integrating DP within LLM-driven synthetic data generation offers a viable balance between privacy protection and data utility. This study provides a foundational methodology and insight into the privacy-preserving capabilities of LLMs, paving the way for compliant and effective ML research and applications.

Have you ever imagined what a corgi-alike coffee machine or a tiger-alike rabbit would look like? In this work, we attempt to answer these questions by exploring a new task called semantic mixing, aiming at blending two different semantics to create a new concept (e.g., corgi + coffee machine -- > corgi-alike coffee machine). Unlike style transfer, where an image is stylized according to the reference style without changing the image content, semantic blending mixes two different concepts in a semantic manner to synthesize a novel concept while preserving the spatial layout and geometry. To this end, we present MagicMix, a simple yet effective solution based on pre-trained text-conditioned diffusion models. Motivated by the progressive generation property of diffusion models where layout/shape emerges at early denoising steps while semantically meaningful details appear at later steps during the denoising process, our method first obtains a coarse layout (either by corrupting an image or denoising from a pure Gaussian noise given a text prompt), followed by injection of conditional prompt for semantic mixing. Our method does not require any spatial mask or re-training, yet is able to synthesize novel objects with high fidelity. To improve the mixing quality, we further devise two simple strategies to provide better control and flexibility over the synthesized content. With our method, we present our results over diverse downstream applications, including semantic style transfer, novel object synthesis, breed mixing, and concept removal, demonstrating the flexibility of our method. More results can be found on the project page https://magicmix.github.io

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this observation, we introduce a novel PEFT method, called Gaussian noise Injected Fine Tuning of Salient Weights (GIFT-SW). Our method updates only salient columns, while injecting Gaussian noise into non-salient ones. To identify these columns, we developeda generalized sensitivity metric that extends and unifies metrics from previous studies. Experiments with LLaMA models demonstrate that GIFT-SW outperforms full fine-tuning and modern PEFT methods under the same computational budget. Moreover, GIFT-SW offers practical advantages to recover performance of models subjected to mixed-precision quantization with keeping salient weights in full precision.

Large language models (LLMs) often produce inaccurate or misleading content-hallucinations. To address this challenge, we introduce Noise-Augmented Fine-Tuning (NoiseFiT), a novel framework that leverages adaptive noise injection based on the signal-to-noise ratio (SNR) to enhance model robustness. In particular, NoiseFiT selectively perturbs layers identified as either high-SNR (more robust) or low-SNR (potentially under-regularized) using a dynamically scaled Gaussian noise. We further propose a hybrid loss that combines standard cross-entropy, soft cross-entropy, and consistency regularization to ensure stable and accurate outputs under noisy training conditions. Our theoretical analysis shows that adaptive noise injection is both unbiased and variance-preserving, providing strong guarantees for convergence in expectation. Empirical results on multiple test and benchmark datasets demonstrate that NoiseFiT significantly reduces hallucination rates, often improving or matching baseline performance in key tasks. These findings highlight the promise of noise-driven strategies for achieving robust, trustworthy language modeling without incurring prohibitive computational overhead. Given the comprehensive and detailed nature of our experiments, we have publicly released the fine-tuning logs, benchmark evaluation artifacts, and source code online at W&B, Hugging Face, and GitHub, respectively, to foster further research, accessibility and reproducibility.

Generative adversarial network (GAN) models can synthesize highquality audio signals while ensuring fast sample generation. However, they are difficult to train and are prone to several issues including mode collapse and divergence. In this paper, we introduce SpecDiff-GAN, a neural vocoder based on HiFi-GAN, which was initially devised for speech synthesis from mel spectrogram. In our model, the training stability is enhanced by means of a forward diffusion process which consists in injecting noise from a Gaussian distribution to both real and fake samples before inputting them to the discriminator. We further improve the model by exploiting a spectrally-shaped noise distribution with the aim to make the discriminator's task more challenging. We then show the merits of our proposed model for speech and music synthesis on several datasets. Our experiments confirm that our model compares favorably in audio quality and efficiency compared to several baselines.

Recently, impressive results have been achieved in 3D scene editing with text instructions based on a 2D diffusion model. However, current diffusion models primarily generate images by predicting noise in the latent space, and the editing is usually applied to the whole image, which makes it challenging to perform delicate, especially localized, editing for 3D scenes. Inspired by recent 3D Gaussian splatting, we propose a systematic framework, named GaussianEditor, to edit 3D scenes delicately via 3D Gaussians with text instructions. Benefiting from the explicit property of 3D Gaussians, we design a series of techniques to achieve delicate editing. Specifically, we first extract the region of interest (RoI) corresponding to the text instruction, aligning it to 3D Gaussians. The Gaussian RoI is further used to control the editing process. Our framework can achieve more delicate and precise editing of 3D scenes than previous methods while enjoying much faster training speed, i.e. within 20 minutes on a single V100 GPU, more than twice as fast as Instruct-NeRF2NeRF (45 minutes -- 2 hours).

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

Diffusion models excel in generating high-quality images. However, current diffusion models struggle to produce reliable images without guidance methods, such as classifier-free guidance (CFG). Are guidance methods truly necessary? Observing that noise obtained via diffusion inversion can reconstruct high-quality images without guidance, we focus on the initial noise of the denoising pipeline. By mapping Gaussian noise to `guidance-free noise', we uncover that small low-magnitude low-frequency components significantly enhance the denoising process, removing the need for guidance and thus improving both inference throughput and memory. Expanding on this, we propose \ours, a novel method that replaces guidance methods with a single refinement of the initial noise. This refined noise enables high-quality image generation without guidance, within the same diffusion pipeline. Our noise-refining model leverages efficient noise-space learning, achieving rapid convergence and strong performance with just 50K text-image pairs. We validate its effectiveness across diverse metrics and analyze how refined noise can eliminate the need for guidance. See our project page: https://cvlab-kaist.github.io/NoiseRefine/.

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which can lead to poor-quality renderings, and reliance on a good initialization. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene-in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) updates by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the 'cloning' of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce a regularizer that promotes the removal of unused Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization.

Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Existing methods to recover model accuracy on analog-digital hardware in the presence of quantization and analog noise include noise-injection training. However, it can be slow in practice, incurring high computational costs, even when starting from pretrained models. We introduce the Sensitivity-Aware Finetuning (SAFT) approach that identifies noise sensitive layers in a model, and uses the information to freeze specific layers for noise-injection training. Our results show that SAFT achieves comparable accuracy to noise-injection training and is 2x to 8x faster.

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity.

Diffusion-based image super-resolution methods have demonstrated significant advantages over GAN-based approaches, particularly in terms of perceptual quality. Building upon a lengthy Markov chain, diffusion-based methods possess remarkable modeling capacity, enabling them to achieve outstanding performance in real-world scenarios. Unlike previous methods that focus on modifying the noise schedule or sampling process to enhance performance, our approach emphasizes the improved utilization of LR information. We find that different regions of the LR image can be viewed as corresponding to different timesteps in a diffusion process, where flat areas are closer to the target HR distribution but edge and texture regions are farther away. In these flat areas, applying a slight noise is more advantageous for the reconstruction. We associate this characteristic with uncertainty and propose to apply uncertainty estimate to guide region-specific noise level control, a technique we refer to as Uncertainty-guided Noise Weighting. Pixels with lower uncertainty (i.e., flat regions) receive reduced noise to preserve more LR information, therefore improving performance. Furthermore, we modify the network architecture of previous methods to develop our Uncertainty-guided Perturbation Super-Resolution (UPSR) model. Extensive experimental results demonstrate that, despite reduced model size and training overhead, the proposed UWSR method outperforms current state-of-the-art methods across various datasets, both quantitatively and qualitatively.

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

Text-to-image diffusion model is a popular paradigm that synthesizes personalized images by providing a text prompt and a random Gaussian noise. While people observe that some noises are ``golden noises'' that can achieve better text-image alignment and higher human preference than others, we still lack a machine learning framework to obtain those golden noises. To learn golden noises for diffusion sampling, we mainly make three contributions in this paper. First, we identify a new concept termed the noise prompt, which aims at turning a random Gaussian noise into a golden noise by adding a small desirable perturbation derived from the text prompt. Following the concept, we first formulate the noise prompt learning framework that systematically learns ``prompted'' golden noise associated with a text prompt for diffusion models. Second, we design a noise prompt data collection pipeline and collect a large-scale noise prompt dataset~(NPD) that contains 100k pairs of random noises and golden noises with the associated text prompts. With the prepared NPD as the training dataset, we trained a small noise prompt network~(NPNet) that can directly learn to transform a random noise into a golden noise. The learned golden noise perturbation can be considered as a kind of prompt for noise, as it is rich in semantic information and tailored to the given text prompt. Third, our extensive experiments demonstrate the impressive effectiveness and generalization of NPNet on improving the quality of synthesized images across various diffusion models, including SDXL, DreamShaper-xl-v2-turbo, and Hunyuan-DiT. Moreover, NPNet is a small and efficient controller that acts as a plug-and-play module with very limited additional inference and computational costs, as it just provides a golden noise instead of a random noise without accessing the original pipeline.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

In recent times, the generation of 3D assets from text prompts has shown impressive results. Both 2D and 3D diffusion models can generate decent 3D objects based on prompts. 3D diffusion models have good 3D consistency, but their quality and generalization are limited as trainable 3D data is expensive and hard to obtain. 2D diffusion models enjoy strong abilities of generalization and fine generation, but the 3D consistency is hard to guarantee. This paper attempts to bridge the power from the two types of diffusion models via the recent explicit and efficient 3D Gaussian splatting representation. A fast 3D generation framework, named as \name, is proposed, where the 3D diffusion model provides point cloud priors for initialization and the 2D diffusion model enriches the geometry and appearance. Operations of noisy point growing and color perturbation are introduced to enhance the initialized Gaussians. Our \name can generate a high-quality 3D instance within 25 minutes on one GPU, much faster than previous methods, while the generated instances can be directly rendered in real time. Demos and code are available at https://taoranyi.com/gaussiandreamer/.

Low-light photography produces images with low signal-to-noise ratios due to limited photons. In such conditions, common approximations like the Gaussian noise model fall short, and many denoising techniques fail to remove noise effectively. Although deep-learning methods perform well, they require large datasets of paired images that are impractical to acquire. As a remedy, synthesizing realistic low-light noise has gained significant attention. In this paper, we investigate the ability of diffusion models to capture the complex distribution of low-light noise. We show that a naive application of conventional diffusion models is inadequate for this task and propose three key adaptations that enable high-precision noise generation without calibration or post-processing: a two-branch architecture to better model signal-dependent and signal-independent noise, the incorporation of positional information to capture fixed-pattern noise, and a tailored diffusion noise schedule. Consequently, our model enables the generation of large datasets for training low-light denoising networks, leading to state-of-the-art performance. Through comprehensive analysis, including statistical evaluation and noise decomposition, we provide deeper insights into the characteristics of the generated data.

Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical distribution information, leading to visually undesirable results. This work addresses the issue by seamlessly integrating a diffusion model with a physics-based exposure model. Different from a vanilla diffusion model that has to perform Gaussian denoising, with the injected physics-based exposure model, our restoration process can directly start from a noisy image instead of pure noise. As such, our method obtains significantly improved performance and reduced inference time compared with vanilla diffusion models. To make full use of the advantages of different intermediate steps, we further propose an adaptive residual layer that effectively screens out the side-effect in the iterative refinement when the intermediate results have been already well-exposed. The proposed framework can work with both real-paired datasets, SOTA noise models, and different backbone networks. Note that, the proposed framework is compatible with real-paired datasets, real/synthetic noise models, and different backbone networks. We evaluate the proposed method on various public benchmarks, achieving promising results with consistent improvements using different exposure models and backbones. Besides, the proposed method achieves better generalization capacity for unseen amplifying ratios and better performance than a larger feedforward neural model when few parameters are adopted.

Vision-Language Models (VLMs) extend the capabilities of Large Language Models (LLMs) by incorporating visual information, yet they remain vulnerable to jailbreak attacks, especially when processing noisy or corrupted images. Although existing VLMs adopt security measures during training to mitigate such attacks, vulnerabilities associated with noise-augmented visual inputs are overlooked. In this work, we identify that missing noise-augmented training causes critical security gaps: many VLMs are susceptible to even simple perturbations such as Gaussian noise. To address this challenge, we propose Robust-VLGuard, a multimodal safety dataset with aligned / misaligned image-text pairs, combined with noise-augmented fine-tuning that reduces attack success rates while preserving functionality of VLM. For stronger optimization-based visual perturbation attacks, we propose DiffPure-VLM, leveraging diffusion models to convert adversarial perturbations into Gaussian-like noise, which can be defended by VLMs with noise-augmented safety fine-tuning. Experimental results demonstrate that the distribution-shifting property of diffusion model aligns well with our fine-tuned VLMs, significantly mitigating adversarial perturbations across varying intensities. The dataset and code are available at https://github.com/JarvisUSTC/DiffPure-RobustVLM.

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits generalization to unseen noise types and levels. Existing approaches attempt to address this with extensive training data and high computational resources but they still suffer from overfitting. To address these issues, we conduct image denoising by utilizing dynamically generated kernels via efficient operations. This approach helps prevent overfitting and improves resilience to unseen noise. Specifically, our method leverages a Feature Extraction Module for robust noise-invariant features, Global Statistics and Local Correlation Modules to capture comprehensive noise characteristics and structural correlations. The Kernel Prediction Module then employs these cues to produce pixel-wise varying kernels adapted to local structures, which are then applied iteratively for denoising. This ensures both efficiency and superior restoration quality. Despite being trained on single-level Gaussian noise, our compact model (~ 0.04 M) excels across diverse noise types and levels, demonstrating the promise of iterative dynamic filtering for practical image denoising.

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and noisy images. Some approaches leverage such unpaired data to train denoisers in a supervised manner by generating synthetic clean-noisy pairs. However, these methods often fall short due to the distribution gap between synthetic and real noisy images. To mitigate this issue, we propose a solution based on input sparsification, specifically using random input masking. Our method, which we refer to as Mask, Inpaint and Denoise (MID), trains a denoiser to simultaneously denoise and inpaint synthetic clean-noisy pairs. On one hand, input sparsification reduces the gap between synthetic and real noisy images. On the other hand, an inpainter trained in a supervised manner can still accurately reconstruct sparse inputs by predicting missing clean pixels using the remaining unmasked pixels. Our approach begins with a synthetic Gaussian noise sampler and iteratively refines it using a noise dataset derived from the denoiser's predictions. The noise dataset is created by subtracting predicted pseudo-clean images from real noisy images at each iteration. The core intuition is that improving the denoiser results in a more accurate noise dataset and, consequently, a better noise sampler. We validate our method through extensive experiments on real-world noisy image datasets, demonstrating competitive performance compared to existing unsupervised denoising methods.

Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial frequencies and condition these components on different text prompts. This produces hybrid images, which change appearance depending on viewing distance. By decomposing an image into three frequency subbands, we can generate hybrid images with three prompts. We also use a decomposition into grayscale and color components to produce images whose appearance changes when they are viewed in grayscale, a phenomena that naturally occurs under dim lighting. And we explore a decomposition by a motion blur kernel, which produces images that change appearance under motion blurring. Our method works by denoising with a composite noise estimate, built from the components of noise estimates conditioned on different prompts. We also show that for certain decompositions, our method recovers prior approaches to compositional generation and spatial control. Finally, we show that we can extend our approach to generate hybrid images from real images. We do this by holding one component fixed and generating the remaining components, effectively solving an inverse problem.

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the choice of image degradation, and in fact an entire family of generative models can be constructed by varying this choice. Even when using completely deterministic degradations (e.g., blur, masking, and more), the training and test-time update rules that underlie diffusion models can be easily generalized to create generative models. The success of these fully deterministic models calls into question the community's understanding of diffusion models, which relies on noise in either gradient Langevin dynamics or variational inference, and paves the way for generalized diffusion models that invert arbitrary processes. Our code is available at https://github.com/arpitbansal297/Cold-Diffusion-Models

Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images. Likelihood-based GMs are attractive due to the possibility to generate new data by a single model evaluation. However, they typically achieve lower sample quality compared to state-of-the-art score-based diffusion models (DMs). This paper provides a significant step in the direction of addressing this limitation. The idea is to borrow one of the strengths of score-based DMs, which is the ability to perform accurate density estimation in low-density regions and to address manifold overfitting by means of data mollification. We connect data mollification through the addition of Gaussian noise to Gaussian homotopy, which is a well-known technique to improve optimization. Data mollification can be implemented by adding one line of code in the optimization loop, and we demonstrate that this provides a boost in generation quality of likelihood-based GMs, without computational overheads. We report results on image data sets with popular likelihood-based GMs, including variants of variational autoencoders and normalizing flows, showing large improvements in FID score.

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to address this via inductive design or data augmentation. However, they can be affected by misleading data, e.g. random noise, and cases where the inference stage data do not match assumptions in the modelled shifts. In this work, by employing a conditional hyperparameter network, we eliminate the need of augmentation, yet maintain robust performance under various levels of Gaussian noise. We demonstrate that our model withstands various input noise levels while producing high-definition reconstructions during the test stage. Moreover, we present a hyperparameter sampling strategy that accelerates the convergence of training. Our proposed method achieves the highest accuracy and image quality in all settings compared to baseline methods.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling

3D Gaussian Splatting (3DGS) has gained significant attention for its real-time, photo-realistic rendering in novel-view synthesis and 3D modeling. However, existing methods struggle with accurately modeling scenes affected by transient objects, leading to artifacts in the rendered images. We identify that the Gaussian densification process, while enhancing scene detail capture, unintentionally contributes to these artifacts by growing additional Gaussians that model transient disturbances. To address this, we propose RobustSplat, a robust solution based on two critical designs. First, we introduce a delayed Gaussian growth strategy that prioritizes optimizing static scene structure before allowing Gaussian splitting/cloning, mitigating overfitting to transient objects in early optimization. Second, we design a scale-cascaded mask bootstrapping approach that first leverages lower-resolution feature similarity supervision for reliable initial transient mask estimation, taking advantage of its stronger semantic consistency and robustness to noise, and then progresses to high-resolution supervision to achieve more precise mask prediction. Extensive experiments on multiple challenging datasets show that our method outperforms existing methods, clearly demonstrating the robustness and effectiveness of our method. Our project page is https://fcyycf.github.io/RobustSplat/.

Achieving high-resolution novel view synthesis (HRNVS) from low-resolution input views is a challenging task due to the lack of high-resolution data. Previous methods optimize high-resolution Neural Radiance Field (NeRF) from low-resolution input views but suffer from slow rendering speed. In this work, we base our method on 3D Gaussian Splatting (3DGS) due to its capability of producing high-quality images at a faster rendering speed. To alleviate the shortage of data for higher-resolution synthesis, we propose to leverage off-the-shelf 2D diffusion priors by distilling the 2D knowledge into 3D with Score Distillation Sampling (SDS). Nevertheless, applying SDS directly to Gaussian-based 3D super-resolution leads to undesirable and redundant 3D Gaussian primitives, due to the randomness brought by generative priors. To mitigate this issue, we introduce two simple yet effective techniques to reduce stochastic disturbances introduced by SDS. Specifically, we 1) shrink the range of diffusion timestep in SDS with an annealing strategy; 2) randomly discard redundant Gaussian primitives during densification. Extensive experiments have demonstrated that our proposed GaussainSR can attain high-quality results for HRNVS with only low-resolution inputs on both synthetic and real-world datasets. Project page: https://chchnii.github.io/GaussianSR/

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an L_2 denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256times256.

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their application becomes more widespread. Here we use the large width Gaussian process limit to analyze the behaviour, at random initialization, of nonlinear activations that induce sparsity in the hidden outputs. A previously unreported form of training instability is proven for arguably two of the most natural candidates for hidden layer sparsification; those being a shifted ReLU (phi(x)=max(0, x-tau) for tauge 0) and soft thresholding (phi(x)=0 for |x|letau and x-sign(x)tau for |x|>tau). We show that this instability is overcome by clipping the nonlinear activation magnitude, at a level prescribed by the shape of the associated Gaussian process variance map. Numerical experiments verify the theory and show that the proposed magnitude clipped sparsifying activations can be trained with training and test fractional sparsity as high as 85\% while retaining close to full accuracy.

Recently, the mainstream practice for training low-light raw image denoising methods has shifted towards employing synthetic data. Noise modeling, which focuses on characterizing the noise distribution of real-world sensors, profoundly influences the effectiveness and practicality of synthetic data. Currently, physics-based noise modeling struggles to characterize the entire real noise distribution, while learning-based noise modeling impractically depends on paired real data. In this paper, we propose a novel strategy: learning the noise model from dark frames instead of paired real data, to break down the data dependency. Based on this strategy, we introduce an efficient physics-guided noise neural proxy (PNNP) to approximate the real-world sensor noise model. Specifically, we integrate physical priors into neural proxies and introduce three efficient techniques: physics-guided noise decoupling (PND), physics-guided proxy model (PPM), and differentiable distribution loss (DDL). PND decouples the dark frame into different components and handles different levels of noise flexibly, which reduces the complexity of noise modeling. PPM incorporates physical priors to constrain the generated noise, which promotes the accuracy of noise modeling. DDL provides explicit and reliable supervision for noise distribution, which promotes the precision of noise modeling. PNNP exhibits powerful potential in characterizing the real noise distribution. Extensive experiments on public datasets demonstrate superior performance in practical low-light raw image denoising. The code will be available at https://github.com/fenghansen/PNNP.

Creating 4D fields of Gaussian Splatting from images or videos is a challenging task due to its under-constrained nature. While the optimization can draw photometric reference from the input videos or be regulated by generative models, directly supervising Gaussian motions remains underexplored. In this paper, we introduce a novel concept, Gaussian flow, which connects the dynamics of 3D Gaussians and pixel velocities between consecutive frames. The Gaussian flow can be efficiently obtained by splatting Gaussian dynamics into the image space. This differentiable process enables direct dynamic supervision from optical flow. Our method significantly benefits 4D dynamic content generation and 4D novel view synthesis with Gaussian Splatting, especially for contents with rich motions that are hard to be handled by existing methods. The common color drifting issue that happens in 4D generation is also resolved with improved Guassian dynamics. Superior visual quality on extensive experiments demonstrates our method's effectiveness. Quantitative and qualitative evaluations show that our method achieves state-of-the-art results on both tasks of 4D generation and 4D novel view synthesis. Project page: https://zerg-overmind.github.io/GaussianFlow.github.io/

One of the key components within diffusion models is the UNet for noise prediction. While several works have explored basic properties of the UNet decoder, its encoder largely remains unexplored. In this work, we conduct the first comprehensive study of the UNet encoder. We empirically analyze the encoder features and provide insights to important questions regarding their changes at the inference process. In particular, we find that encoder features change gently, whereas the decoder features exhibit substantial variations across different time-steps. This finding inspired us to omit the encoder at certain adjacent time-steps and reuse cyclically the encoder features in the previous time-steps for the decoder. Further based on this observation, we introduce a simple yet effective encoder propagation scheme to accelerate the diffusion sampling for a diverse set of tasks. By benefiting from our propagation scheme, we are able to perform in parallel the decoder at certain adjacent time-steps. Additionally, we introduce a prior noise injection method to improve the texture details in the generated image. Besides the standard text-to-image task, we also validate our approach on other tasks: text-to-video, personalized generation and reference-guided generation. Without utilizing any knowledge distillation technique, our approach accelerates both the Stable Diffusion (SD) and the DeepFloyd-IF models sampling by 41% and 24% respectively, while maintaining high-quality generation performance. Our code is available in https://github.com/hutaiHang/Faster-Diffusion{FasterDiffusion}.

The 3D Gaussian Splatting (3DGS) gained its popularity recently by combining the advantages of both primitive-based and volumetric 3D representations, resulting in improved quality and efficiency for 3D scene rendering. However, 3DGS is not alias-free, and its rendering at varying resolutions could produce severe blurring or jaggies. This is because 3DGS treats each pixel as an isolated, single point rather than as an area, causing insensitivity to changes in the footprints of pixels. Consequently, this discrete sampling scheme inevitably results in aliasing, owing to the restricted sampling bandwidth. In this paper, we derive an analytical solution to address this issue. More specifically, we use a conditioned logistic function as the analytic approximation of the cumulative distribution function (CDF) in a one-dimensional Gaussian signal and calculate the Gaussian integral by subtracting the CDFs. We then introduce this approximation in the two-dimensional pixel shading, and present Analytic-Splatting, which analytically approximates the Gaussian integral within the 2D-pixel window area to better capture the intensity response of each pixel. Moreover, we use the approximated response of the pixel window integral area to participate in the transmittance calculation of volume rendering, making Analytic-Splatting sensitive to the changes in pixel footprint at different resolutions. Experiments on various datasets validate that our approach has better anti-aliasing capability that gives more details and better fidelity.

Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Tuning-free long video diffusion has been proposed to generate extended-duration videos with enriched content by reusing the knowledge from pre-trained short video diffusion model without retraining. However, most works overlook the fine-grained long-term video consistency modeling, resulting in limited scene consistency (i.e., unreasonable object or background transitions), especially with multiple text inputs. To mitigate this, we propose the Consistency Noise Injection, dubbed CoNo, which introduces the "look-back" mechanism to enhance the fine-grained scene transition between different video clips, and designs the long-term consistency regularization to eliminate the content shifts when extending video contents through noise prediction. In particular, the "look-back" mechanism breaks the noise scheduling process into three essential parts, where one internal noise prediction part is injected into two video-extending parts, intending to achieve a fine-grained transition between two video clips. The long-term consistency regularization focuses on explicitly minimizing the pixel-wise distance between the predicted noises of the extended video clip and the original one, thereby preventing abrupt scene transitions. Extensive experiments have shown the effectiveness of the above strategies by performing long-video generation under both single- and multi-text prompt conditions. The project has been available in https://wxrui182.github.io/CoNo.github.io/.

Generating high-quality 3D content requires models capable of learning robust distributions of complex scenes and the real-world objects within them. Recent Gaussian-based 3D reconstruction techniques have achieved impressive results in recovering high-fidelity 3D assets from sparse input images by predicting 3D Gaussians in a feed-forward manner. However, these techniques often lack the extensive priors and expressiveness offered by Diffusion Models. On the other hand, 2D Diffusion Models, which have been successfully applied to denoise multiview images, show potential for generating a wide range of photorealistic 3D outputs but still fall short on explicit 3D priors and consistency. In this work, we aim to bridge these two approaches by introducing DSplats, a novel method that directly denoises multiview images using Gaussian Splat-based Reconstructors to produce a diverse array of realistic 3D assets. To harness the extensive priors of 2D Diffusion Models, we incorporate a pretrained Latent Diffusion Model into the reconstructor backbone to predict a set of 3D Gaussians. Additionally, the explicit 3D representation embedded in the denoising network provides a strong inductive bias, ensuring geometrically consistent novel view generation. Our qualitative and quantitative experiments demonstrate that DSplats not only produces high-quality, spatially consistent outputs, but also sets a new standard in single-image to 3D reconstruction. When evaluated on the Google Scanned Objects dataset, DSplats achieves a PSNR of 20.38, an SSIM of 0.842, and an LPIPS of 0.109.

Recently, 3D Gaussian splatting (3D-GS) has achieved great success in reconstructing and rendering real-world scenes. To transfer the high rendering quality to generation tasks, a series of research works attempt to generate 3D-Gaussian assets from text. However, the generated assets have not achieved the same quality as those in reconstruction tasks. We observe that Gaussians tend to grow without control as the generation process may cause indeterminacy. Aiming at highly enhancing the generation quality, we propose a novel framework named GaussianDreamerPro. The main idea is to bind Gaussians to reasonable geometry, which evolves over the whole generation process. Along different stages of our framework, both the geometry and appearance can be enriched progressively. The final output asset is constructed with 3D Gaussians bound to mesh, which shows significantly enhanced details and quality compared with previous methods. Notably, the generated asset can also be seamlessly integrated into downstream manipulation pipelines, e.g. animation, composition, and simulation etc., greatly promoting its potential in wide applications. Demos are available at https://taoranyi.com/gaussiandreamerpro/.

In this work, we build upon our previous publication and use diffusion-based generative models for speech enhancement. We present a detailed overview of the diffusion process that is based on a stochastic differential equation and delve into an extensive theoretical examination of its implications. Opposed to usual conditional generation tasks, we do not start the reverse process from pure Gaussian noise but from a mixture of noisy speech and Gaussian noise. This matches our forward process which moves from clean speech to noisy speech by including a drift term. We show that this procedure enables using only 30 diffusion steps to generate high-quality clean speech estimates. By adapting the network architecture, we are able to significantly improve the speech enhancement performance, indicating that the network, rather than the formalism, was the main limitation of our original approach. In an extensive cross-dataset evaluation, we show that the improved method can compete with recent discriminative models and achieves better generalization when evaluating on a different corpus than used for training. We complement the results with an instrumental evaluation using real-world noisy recordings and a listening experiment, in which our proposed method is rated best. Examining different sampler configurations for solving the reverse process allows us to balance the performance and computational speed of the proposed method. Moreover, we show that the proposed method is also suitable for dereverberation and thus not limited to additive background noise removal. Code and audio examples are available online, see https://github.com/sp-uhh/sgmse

Recent text-guided diffusion models provide powerful image generation capabilities. Currently, a massive effort is given to enable the modification of these images using text only as means to offer intuitive and versatile editing. To edit a real image using these state-of-the-art tools, one must first invert the image with a meaningful text prompt into the pretrained model's domain. In this paper, we introduce an accurate inversion technique and thus facilitate an intuitive text-based modification of the image. Our proposed inversion consists of two novel key components: (i) Pivotal inversion for diffusion models. While current methods aim at mapping random noise samples to a single input image, we use a single pivotal noise vector for each timestamp and optimize around it. We demonstrate that a direct inversion is inadequate on its own, but does provide a good anchor for our optimization. (ii) NULL-text optimization, where we only modify the unconditional textual embedding that is used for classifier-free guidance, rather than the input text embedding. This allows for keeping both the model weights and the conditional embedding intact and hence enables applying prompt-based editing while avoiding the cumbersome tuning of the model's weights. Our Null-text inversion, based on the publicly available Stable Diffusion model, is extensively evaluated on a variety of images and prompt editing, showing high-fidelity editing of real images.

Diffusion models have demonstrated compelling generation quality by optimizing the variational lower bound through a simple denoising score matching loss. In this paper, we provide theoretical evidence that the prevailing practice of using a constant loss weight strategy in diffusion models leads to biased estimation during the training phase. Simply optimizing the denoising network to predict Gaussian noise with constant weighting may hinder precise estimations of original images. To address the issue, we propose an elegant and effective weighting strategy grounded in the theoretically unbiased principle. Moreover, we conduct a comprehensive and systematic exploration to dissect the inherent bias problem deriving from constant weighting loss from the perspectives of its existence, impact and reasons. These analyses are expected to advance our understanding and demystify the inner workings of diffusion models. Through empirical evaluation, we demonstrate that our proposed debiased estimation method significantly enhances sample quality without the reliance on complex techniques, and exhibits improved efficiency compared to the baseline method both in training and sampling processes.

Diffusion-based generative models have recently gained attention in speech enhancement (SE), providing an alternative to conventional supervised methods. These models transform clean speech training samples into Gaussian noise centered at noisy speech, and subsequently learn a parameterized model to reverse this process, conditionally on noisy speech. Unlike supervised methods, generative-based SE approaches usually rely solely on an unsupervised loss, which may result in less efficient incorporation of conditioned noisy speech. To address this issue, we propose augmenting the original diffusion training objective with a mean squared error (MSE) loss, measuring the discrepancy between estimated enhanced speech and ground-truth clean speech at each reverse process iteration. Experimental results demonstrate the effectiveness of our proposed methodology.

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as Theta_n(1{n}). Finally, this rate is shown to be in fact Bayes-optimal.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

In recent years, 3D Gaussian splatting has emerged as a powerful technique for 3D reconstruction and generation, known for its fast and high-quality rendering capabilities. To address these shortcomings, this paper introduces a novel diffusion-based framework, GVGEN, designed to efficiently generate 3D Gaussian representations from text input. We propose two innovative techniques:(1) Structured Volumetric Representation. We first arrange disorganized 3D Gaussian points as a structured form GaussianVolume. This transformation allows the capture of intricate texture details within a volume composed of a fixed number of Gaussians. To better optimize the representation of these details, we propose a unique pruning and densifying method named the Candidate Pool Strategy, enhancing detail fidelity through selective optimization. (2) Coarse-to-fine Generation Pipeline. To simplify the generation of GaussianVolume and empower the model to generate instances with detailed 3D geometry, we propose a coarse-to-fine pipeline. It initially constructs a basic geometric structure, followed by the prediction of complete Gaussian attributes. Our framework, GVGEN, demonstrates superior performance in qualitative and quantitative assessments compared to existing 3D generation methods. Simultaneously, it maintains a fast generation speed (sim7 seconds), effectively striking a balance between quality and efficiency.

3D editing plays a crucial role in many areas such as gaming and virtual reality. Traditional 3D editing methods, which rely on representations like meshes and point clouds, often fall short in realistically depicting complex scenes. On the other hand, methods based on implicit 3D representations, like Neural Radiance Field (NeRF), render complex scenes effectively but suffer from slow processing speeds and limited control over specific scene areas. In response to these challenges, our paper presents GaussianEditor, an innovative and efficient 3D editing algorithm based on Gaussian Splatting (GS), a novel 3D representation. GaussianEditor enhances precision and control in editing through our proposed Gaussian semantic tracing, which traces the editing target throughout the training process. Additionally, we propose Hierarchical Gaussian splatting (HGS) to achieve stabilized and fine results under stochastic generative guidance from 2D diffusion models. We also develop editing strategies for efficient object removal and integration, a challenging task for existing methods. Our comprehensive experiments demonstrate GaussianEditor's superior control, efficacy, and rapid performance, marking a significant advancement in 3D editing. Project Page: https://buaacyw.github.io/gaussian-editor/

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

3D Gaussians have recently emerged as an efficient representation for novel view synthesis. This work studies its editability with a particular focus on the inpainting task, which aims to supplement an incomplete set of 3D Gaussians with additional points for visually harmonious rendering. Compared to 2D inpainting, the crux of inpainting 3D Gaussians is to figure out the rendering-relevant properties of the introduced points, whose optimization largely benefits from their initial 3D positions. To this end, we propose to guide the point initialization with an image-conditioned depth completion model, which learns to directly restore the depth map based on the observed image. Such a design allows our model to fill in depth values at an aligned scale with the original depth, and also to harness strong generalizability from largescale diffusion prior. Thanks to the more accurate depth completion, our approach, dubbed InFusion, surpasses existing alternatives with sufficiently better fidelity and efficiency under various complex scenarios. We further demonstrate the effectiveness of InFusion with several practical applications, such as inpainting with user-specific texture or with novel object insertion.

Denoising diffusion probabilistic models have been recently proposed to generate high-quality samples by estimating the gradient of the data density. The framework defines the prior noise as a standard Gaussian distribution, whereas the corresponding data distribution may be more complicated than the standard Gaussian distribution, which potentially introduces inefficiency in denoising the prior noise into the data sample because of the discrepancy between the data and the prior. In this paper, we propose PriorGrad to improve the efficiency of the conditional diffusion model for speech synthesis (for example, a vocoder using a mel-spectrogram as the condition) by applying an adaptive prior derived from the data statistics based on the conditional information. We formulate the training and sampling procedures of PriorGrad and demonstrate the advantages of an adaptive prior through a theoretical analysis. Focusing on the speech synthesis domain, we consider the recently proposed diffusion-based speech generative models based on both the spectral and time domains and show that PriorGrad achieves faster convergence and inference with superior performance, leading to an improved perceptual quality and robustness to a smaller network capacity, and thereby demonstrating the efficiency of a data-dependent adaptive prior.

Generative modeling aims to transform random noise into structured outputs. In this work, we enhance video diffusion models by allowing motion control via structured latent noise sampling. This is achieved by just a change in data: we pre-process training videos to yield structured noise. Consequently, our method is agnostic to diffusion model design, requiring no changes to model architectures or training pipelines. Specifically, we propose a novel noise warping algorithm, fast enough to run in real time, that replaces random temporal Gaussianity with correlated warped noise derived from optical flow fields, while preserving the spatial Gaussianity. The efficiency of our algorithm enables us to fine-tune modern video diffusion base models using warped noise with minimal overhead, and provide a one-stop solution for a wide range of user-friendly motion control: local object motion control, global camera movement control, and motion transfer. The harmonization between temporal coherence and spatial Gaussianity in our warped noise leads to effective motion control while maintaining per-frame pixel quality. Extensive experiments and user studies demonstrate the advantages of our method, making it a robust and scalable approach for controlling motion in video diffusion models. Video results are available on our webpage: https://vgenai-netflix-eyeline-research.github.io/Go-with-the-Flow. Source code and model checkpoints are available on GitHub: https://github.com/VGenAI-Netflix-Eyeline-Research/Go-with-the-Flow.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

Text-guided diffusion models have become a popular tool in image synthesis, known for producing high-quality and diverse images. However, their application to editing real images often encounters hurdles primarily due to the text condition deteriorating the reconstruction quality and subsequently affecting editing fidelity. Null-text Inversion (NTI) has made strides in this area, but it fails to capture spatial context and requires computationally intensive per-timestep optimization. Addressing these challenges, we present Noise Map Guidance (NMG), an inversion method rich in a spatial context, tailored for real-image editing. Significantly, NMG achieves this without necessitating optimization, yet preserves the editing quality. Our empirical investigations highlight NMG's adaptability across various editing techniques and its robustness to variants of DDIM inversions.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

This study presents a new image super-resolution (SR) technique based on diffusion inversion, aiming at harnessing the rich image priors encapsulated in large pre-trained diffusion models to improve SR performance. We design a Partial noise Prediction strategy to construct an intermediate state of the diffusion model, which serves as the starting sampling point. Central to our approach is a deep noise predictor to estimate the optimal noise maps for the forward diffusion process. Once trained, this noise predictor can be used to initialize the sampling process partially along the diffusion trajectory, generating the desirable high-resolution result. Compared to existing approaches, our method offers a flexible and efficient sampling mechanism that supports an arbitrary number of sampling steps, ranging from one to five. Even with a single sampling step, our method demonstrates superior or comparable performance to recent state-of-the-art approaches. The code and model are publicly available at https://github.com/zsyOAOA/InvSR.

Gaussian Splatting has become a popular technique for various 3D Computer Vision tasks, including novel view synthesis, scene reconstruction, and dynamic scene rendering. However, the challenge of natural-looking object insertion, where the object's appearance seamlessly matches the scene, remains unsolved. In this work, we propose a method, dubbed D3DR, for inserting a 3DGS-parametrized object into 3DGS scenes while correcting its lighting, shadows, and other visual artifacts to ensure consistency, a problem that has not been successfully addressed before. We leverage advances in diffusion models, which, trained on real-world data, implicitly understand correct scene lighting. After inserting the object, we optimize a diffusion-based Delta Denoising Score (DDS)-inspired objective to adjust its 3D Gaussian parameters for proper lighting correction. Utilizing diffusion model personalization techniques to improve optimization quality, our approach ensures seamless object insertion and natural appearance. Finally, we demonstrate the method's effectiveness by comparing it to existing approaches, achieving 0.5 PSNR and 0.15 SSIM improvements in relighting quality.

When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of Transformer-based models that have achieved notable state-of-the-art results on various image tasks. However, deep learning-based methods often suffer from a lack of generalization ability. For example, deep models trained on Gaussian noise may perform poorly when tested on other noise distributions. To address this issue, we present a novel approach to enhance the generalization performance of denoising networks, known as masked training. Our method involves masking random pixels of the input image and reconstructing the missing information during training. We also mask out the features in the self-attention layers to avoid the impact of training-testing inconsistency. Our approach exhibits better generalization ability than other deep learning models and is directly applicable to real-world scenarios. Additionally, our interpretability analysis demonstrates the superiority of our method.

Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed combining the benefits of both primitive-based representations and volumetric representations. However, it often leads to heavily redundant Gaussians that try to fit every training view, neglecting the underlying scene geometry. Consequently, the resulting model becomes less robust to significant view changes, texture-less area and lighting effects. We introduce Scaffold-GS, which uses anchor points to distribute local 3D Gaussians, and predicts their attributes on-the-fly based on viewing direction and distance within the view frustum. Anchor growing and pruning strategies are developed based on the importance of neural Gaussians to reliably improve the scene coverage. We show that our method effectively reduces redundant Gaussians while delivering high-quality rendering. We also demonstrates an enhanced capability to accommodate scenes with varying levels-of-detail and view-dependent observations, without sacrificing the rendering speed.

Four-dimensional computed tomography (4D CT) reconstruction is crucial for capturing dynamic anatomical changes but faces inherent limitations from conventional phase-binning workflows. Current methods discretize temporal resolution into fixed phases with respiratory gating devices, introducing motion misalignment and restricting clinical practicality. In this paper, We propose X^2-Gaussian, a novel framework that enables continuous-time 4D-CT reconstruction by integrating dynamic radiative Gaussian splatting with self-supervised respiratory motion learning. Our approach models anatomical dynamics through a spatiotemporal encoder-decoder architecture that predicts time-varying Gaussian deformations, eliminating phase discretization. To remove dependency on external gating devices, we introduce a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization. Extensive experiments demonstrate state-of-the-art performance, achieving a 9.93 dB PSNR gain over traditional methods and 2.25 dB improvement against prior Gaussian splatting techniques. By unifying continuous motion modeling with hardware-free period learning, X^2-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging. Project website at: https://x2-gaussian.github.io/.

Most advances in 3D Generative Adversarial Networks (3D GANs) largely depend on ray casting-based volume rendering, which incurs demanding rendering costs. One promising alternative is rasterization-based 3D Gaussian Splatting (3D-GS), providing a much faster rendering speed and explicit 3D representation. In this paper, we exploit Gaussian as a 3D representation for 3D GANs by leveraging its efficient and explicit characteristics. However, in an adversarial framework, we observe that a na\"ive generator architecture suffers from training instability and lacks the capability to adjust the scale of Gaussians. This leads to model divergence and visual artifacts due to the absence of proper guidance for initialized positions of Gaussians and densification to manage their scales adaptively. To address these issues, we introduce a generator architecture with a hierarchical multi-scale Gaussian representation that effectively regularizes the position and scale of generated Gaussians. Specifically, we design a hierarchy of Gaussians where finer-level Gaussians are parameterized by their coarser-level counterparts; the position of finer-level Gaussians would be located near their coarser-level counterparts, and the scale would monotonically decrease as the level becomes finer, modeling both coarse and fine details of the 3D scene. Experimental results demonstrate that ours achieves a significantly faster rendering speed (x100) compared to state-of-the-art 3D consistent GANs with comparable 3D generation capability. Project page: https://hse1032.github.io/gsgan.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion. Recently, the emerging diffusion model has achieved state-of-the-art performance in various tasks and demonstrates great potential for image denoising. However, stimulating diffusion models for image denoising is not straightforward and requires solving several critical problems. For one thing, the input inconsistency hinders the connection between diffusion models and image denoising. For another, the content inconsistency between the generated image and the desired denoised image introduces distortion. To tackle these problems, we present a novel strategy called the Diffusion Model for Image Denoising (DMID) by understanding and rethinking the diffusion model from a denoising perspective. Our DMID strategy includes an adaptive embedding method that embeds the noisy image into a pre-trained unconditional diffusion model and an adaptive ensembling method that reduces distortion in the denoised image. Our DMID strategy achieves state-of-the-art performance on both distortion-based and perception-based metrics, for both Gaussian and real-world image denoising.The code is available at https://github.com/Li-Tong-621/DMID.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

Generative models have reached an advanced stage where they can produce remarkably realistic images. However, this remarkable generative capability also introduces the risk of disseminating false or misleading information. Notably, existing image detectors for generated images encounter challenges such as low accuracy and limited generalization. This paper seeks to address this issue by seeking a representation with strong generalization capabilities to enhance the detection of generated images. Our investigation has revealed that real and generated images display distinct latent Gaussian representations when subjected to an inverse diffusion process within a pre-trained diffusion model. Exploiting this disparity, we can amplify subtle artifacts in generated images. Building upon this insight, we introduce a novel image representation known as Diffusion Noise Feature (DNF). DNF is extracted from the estimated noise generated during the inverse diffusion process. A simple classifier, e.g., ResNet50, trained on DNF achieves high accuracy, robustness, and generalization capabilities for detecting generated images (even the corresponding generator is built with datasets/structures that are not seen during the classifier's training). We conducted experiments using four training datasets and five testsets, achieving state-of-the-art detection performance.

3D Gaussian Splatting is a new method for modeling and rendering 3D radiance fields that achieves much faster learning and rendering time compared to SOTA NeRF methods. However, it comes with a drawback in the much larger storage demand compared to NeRF methods since it needs to store the parameters for several 3D Gaussians. We notice that many Gaussians may share similar parameters, so we introduce a simple vector quantization method based on \kmeans algorithm to quantize the Gaussian parameters. Then, we store the small codebook along with the index of the code for each Gaussian. Moreover, we compress the indices further by sorting them and using a method similar to run-length encoding. We do extensive experiments on standard benchmarks as well as a new benchmark which is an order of magnitude larger than the standard benchmarks. We show that our simple yet effective method can reduce the storage cost for the original 3D Gaussian Splatting method by a factor of almost 20times with a very small drop in the quality of rendered images.

We present a novel generative approach based on Denoising Diffusion Models (DDMs), which produces high-quality image samples along with their losslessly compressed bit-stream representations. This is obtained by replacing the standard Gaussian noise sampling in the reverse diffusion with a selection of noise samples from pre-defined codebooks of fixed iid Gaussian vectors. Surprisingly, we find that our method, termed Denoising Diffusion Codebook Model (DDCM), retains sample quality and diversity of standard DDMs, even for extremely small codebooks. We leverage DDCM and pick the noises from the codebooks that best match a given image, converting our generative model into a highly effective lossy image codec achieving state-of-the-art perceptual image compression results. More generally, by setting other noise selections rules, we extend our compression method to any conditional image generation task (e.g., image restoration), where the generated images are produced jointly with their condensed bit-stream representations. Our work is accompanied by a mathematical interpretation of the proposed compressed conditional generation schemes, establishing a connection with score-based approximations of posterior samplers for the tasks considered.

We propose a method to enhance 3D Gaussian Splatting (3DGS)~Kerbl2023, addressing challenges in initialization, optimization, and density control. Gaussian Splatting is an alternative for rendering realistic images while supporting real-time performance, and it has gained popularity due to its explicit 3D Gaussian representation. However, 3DGS heavily depends on accurate initialization and faces difficulties in optimizing unstructured Gaussian distributions into ordered surfaces, with limited adaptive density control mechanism proposed so far. Our first key contribution is a geometry-guided initialization to predict Gaussian parameters, ensuring precise placement and faster convergence. We then introduce a surface-aligned optimization strategy to refine Gaussian placement, improving geometric accuracy and aligning with the surface normals of the scene. Finally, we present a dynamic adaptive density control mechanism that adjusts Gaussian density based on regional complexity, for visual fidelity. These innovations enable our method to achieve high-fidelity real-time rendering and significant improvements in visual quality, even in complex scenes. Our method demonstrates comparable or superior results to state-of-the-art methods, rendering high-fidelity images in real time.

Image watermark techniques provide an effective way to assert ownership, deter misuse, and trace content sources, which has become increasingly essential in the era of large generative models. A critical attribute of watermark techniques is their robustness against various manipulations. In this paper, we introduce a watermark removal approach capable of effectively nullifying the state of the art watermarking techniques. Our primary insight involves regenerating the watermarked image starting from a clean Gaussian noise via a controllable diffusion model, utilizing the extracted semantic and spatial features from the watermarked image. The semantic control adapter and the spatial control network are specifically trained to control the denoising process towards ensuring image quality and enhancing consistency between the cleaned image and the original watermarked image. To achieve a smooth trade-off between watermark removal performance and image consistency, we further propose an adjustable and controllable regeneration scheme. This scheme adds varying numbers of noise steps to the latent representation of the watermarked image, followed by a controlled denoising process starting from this noisy latent representation. As the number of noise steps increases, the latent representation progressively approaches clean Gaussian noise, facilitating the desired trade-off. We apply our watermark removal methods across various watermarking techniques, and the results demonstrate that our methods offer superior visual consistency/quality and enhanced watermark removal performance compared to existing regeneration approaches.

Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

Latent Video Diffusion Models (LVDMs) achieve high-quality generation but are sensitive to imperfect conditioning, which causes semantic drift and temporal incoherence on noisy, web-scale video-text datasets. We introduce CAT-LVDM, the first corruption-aware training framework for LVDMs that improves robustness through structured, data-aligned noise injection. Our method includes Batch-Centered Noise Injection (BCNI), which perturbs embeddings along intra-batch semantic directions to preserve temporal consistency. BCNI is especially effective on caption-rich datasets like WebVid-2M, MSR-VTT, and MSVD. We also propose Spectrum-Aware Contextual Noise (SACN), which injects noise along dominant spectral directions to improve low-frequency smoothness, showing strong results on UCF-101. On average, BCNI reduces FVD by 31.9% across WebVid-2M, MSR-VTT, and MSVD, while SACN yields a 12.3% improvement on UCF-101. Ablation studies confirm the benefit of low-rank, data-aligned noise. Our theoretical analysis further explains how such perturbations tighten entropy, Wasserstein, score-drift, mixing-time, and generalization bounds. CAT-LVDM establishes a principled, scalable training approach for robust video diffusion under multimodal noise. Code and models: https://github.com/chikap421/catlvdm

X-ray is widely applied for transmission imaging due to its stronger penetration than natural light. When rendering novel view X-ray projections, existing methods mainly based on NeRF suffer from long training time and slow inference speed. In this paper, we propose a 3D Gaussian splatting-based framework, namely X-Gaussian, for X-ray novel view synthesis. Firstly, we redesign a radiative Gaussian point cloud model inspired by the isotropic nature of X-ray imaging. Our model excludes the influence of view direction when learning to predict the radiation intensity of 3D points. Based on this model, we develop a Differentiable Radiative Rasterization (DRR) with CUDA implementation. Secondly, we customize an Angle-pose Cuboid Uniform Initialization (ACUI) strategy that directly uses the parameters of the X-ray scanner to compute the camera information and then uniformly samples point positions within a cuboid enclosing the scanned object. Experiments show that our X-Gaussian outperforms state-of-the-art methods by 6.5 dB while enjoying less than 15% training time and over 73x inference speed. The application on sparse-view CT reconstruction also reveals the practical values of our method. Code and models will be publicly available at https://github.com/caiyuanhao1998/X-Gaussian . A video demo of the training process visualization is at https://www.youtube.com/watch?v=gDVf_Ngeghg .

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

The progress in generative models, particularly Generative Adversarial Networks (GANs), opened new possibilities for image generation but raised concerns about potential malicious uses, especially in sensitive areas like medical imaging. This study introduces MITS-GAN, a novel approach to prevent tampering in medical images, with a specific focus on CT scans. The approach disrupts the output of the attacker's CT-GAN architecture by introducing finely tuned perturbations that are imperceptible to the human eye. Specifically, the proposed approach involves the introduction of appropriate Gaussian noise to the input as a protective measure against various attacks. Our method aims to enhance tamper resistance, comparing favorably to existing techniques. Experimental results on a CT scan demonstrate MITS-GAN's superior performance, emphasizing its ability to generate tamper-resistant images with negligible artifacts. As image tampering in medical domains poses life-threatening risks, our proactive approach contributes to the responsible and ethical use of generative models. This work provides a foundation for future research in countering cyber threats in medical imaging. Models and codes are publicly available on https://iplab.dmi.unict.it/MITS-GAN-2024/.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show that the former allocates a model's capacity towards a subspace of the data explaining the observed variance--a subspace with uninformative features for the latter. For example, the supervised TinyImagenet task with images projected onto the top subspace explaining 90\% of the pixel variance can be solved with 45\% test accuracy. Using the bottom subspace instead, accounting for only 20\% of the pixel variance, reaches 55\% test accuracy. The features for perception being learned last explains the need for long training time, e.g., with Masked Autoencoders. Learning by denoising is a popular strategy to alleviate that misalignment. We prove that while some noise strategies such as masking are indeed beneficial, others such as additive Gaussian noise are not. Yet, even in the case of masking, we find that the benefits vary as a function of the mask's shape, ratio, and the considered dataset. While tuning the noise strategy without knowledge of the perception task seems challenging, we provide first clues on how to detect if a noise strategy is never beneficial regardless of the perception task.

Recent advances in diffusion models have introduced a new era of text-guided image manipulation, enabling users to create realistic edited images with simple textual prompts. However, there is significant concern about the potential misuse of these methods, especially in creating misleading or harmful content. Although recent defense strategies, which introduce imperceptible adversarial noise to induce model failure, have shown promise, they remain ineffective against more sophisticated manipulations, such as editing with a mask. In this work, we propose DiffusionGuard, a robust and effective defense method against unauthorized edits by diffusion-based image editing models, even in challenging setups. Through a detailed analysis of these models, we introduce a novel objective that generates adversarial noise targeting the early stage of the diffusion process. This approach significantly improves the efficiency and effectiveness of adversarial noises. We also introduce a mask-augmentation technique to enhance robustness against various masks during test time. Finally, we introduce a comprehensive benchmark designed to evaluate the effectiveness and robustness of methods in protecting against privacy threats in realistic scenarios. Through extensive experiments, we show that our method achieves stronger protection and improved mask robustness with lower computational costs compared to the strongest baseline. Additionally, our method exhibits superior transferability and better resilience to noise removal techniques compared to all baseline methods. Our source code is publicly available at https://github.com/choi403/DiffusionGuard.

We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.

We present an approach to mitigating the risks of malicious image editing posed by large diffusion models. The key idea is to immunize images so as to make them resistant to manipulation by these models. This immunization relies on injection of imperceptible adversarial perturbations designed to disrupt the operation of the targeted diffusion models, forcing them to generate unrealistic images. We provide two methods for crafting such perturbations, and then demonstrate their efficacy. Finally, we discuss a policy component necessary to make our approach fully effective and practical -- one that involves the organizations developing diffusion models, rather than individual users, to implement (and support) the immunization process.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

In order to improve the quality of synthesized videos, currently, one predominant method involves retraining an expert diffusion model and then implementing a noising-denoising process for refinement. Despite the significant training costs, maintaining consistency of content between the original and enhanced videos remains a major challenge. To tackle this challenge, we propose a novel formulation that considers both visual quality and consistency of content. Consistency of content is ensured by a proposed loss function that maintains the structure of the input, while visual quality is improved by utilizing the denoising process of pretrained diffusion models. To address the formulated optimization problem, we have developed a plug-and-play noise optimization strategy, referred to as Noise Calibration. By refining the initial random noise through a few iterations, the content of original video can be largely preserved, and the enhancement effect demonstrates a notable improvement. Extensive experiments have demonstrated the effectiveness of the proposed method.

Recently, image-to-3D approaches have significantly advanced the generation quality and speed of 3D assets based on large reconstruction models, particularly 3D Gaussian reconstruction models. Existing large 3D Gaussian models directly map 2D image to 3D Gaussian parameters, while regressing 2D image to 3D Gaussian representations is challenging without 3D priors. In this paper, we propose a large Point-to-Gaussian model, that inputs the initial point cloud produced from large 3D diffusion model conditional on 2D image to generate the Gaussian parameters, for image-to-3D generation. The point cloud provides initial 3D geometry prior for Gaussian generation, thus significantly facilitating image-to-3D Generation. Moreover, we present the Attention mechanism, Projection mechanism, and Point feature extractor, dubbed as APP block, for fusing the image features with point cloud features. The qualitative and quantitative experiments extensively demonstrate the effectiveness of the proposed approach on GSO and Objaverse datasets, and show the proposed method achieves state-of-the-art performance.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at https://voldemort108x.github.io/hetero_uncertainty/.

We propose a new uncertainty estimator for gradient-free optimisation of black-box simulators using deep generative surrogate models. Optimisation of these simulators is especially challenging for stochastic simulators and higher dimensions. To address these issues, we utilise a deep generative surrogate approach to model the black box response for the entire parameter space. We then leverage this knowledge to estimate the proposed uncertainty based on the Wasserstein distance - the Wasserstein uncertainty. This approach is employed in a posterior agnostic gradient-free optimisation algorithm that minimises regret over the entire parameter space. A series of tests were conducted to demonstrate that our method is more robust to the shape of both the black box function and the stochastic response of the black box than state-of-the-art methods, such as efficient global optimisation with a deep Gaussian process surrogate.

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness. Probabilistic models with more parameters, such as the Gaussian mixture models, can fit the distribution of latent variables more precisely, but the corresponding complexity will also be higher. To balance between compression performance and complexity, we extend the Gaussian model to the generalized Gaussian model for more flexible latent distribution modeling, introducing only one additional shape parameter, beta, than the Gaussian model. To enhance the performance of the generalized Gaussian model by alleviating the train-test mismatch, we propose improved training methods, including beta-dependent lower bounds for scale parameters and gradient rectification. Our proposed generalized Gaussian model, coupled with the improved training methods, is demonstrated to outperform the Gaussian and Gaussian mixture models on a variety of learned image compression methods.

This report presents the comprehensive implementation, evaluation, and optimization of Denoising Diffusion Probabilistic Models (DDPMs) and Denoising Diffusion Implicit Models (DDIMs), which are state-of-the-art generative models. During inference, these models take random noise as input and iteratively generate high-quality images as output. The study focuses on enhancing their generative capabilities by incorporating advanced techniques such as Classifier-Free Guidance (CFG), Latent Diffusion Models with Variational Autoencoders (VAE), and alternative noise scheduling strategies. The motivation behind this work is the growing demand for efficient and scalable generative AI models that can produce realistic images across diverse datasets, addressing challenges in applications such as art creation, image synthesis, and data augmentation. Evaluations were conducted on datasets including CIFAR-10 and ImageNet-100, with a focus on improving inference speed, computational efficiency, and image quality metrics like Frechet Inception Distance (FID). Results demonstrate that DDIM + CFG achieves faster inference and superior image quality. Challenges with VAE and noise scheduling are also highlighted, suggesting opportunities for future optimization. This work lays the groundwork for developing scalable, efficient, and high-quality generative AI systems to benefit industries ranging from entertainment to robotics.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, potentially benefiting other sequential algorithms. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (R\'enyi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any epsilon-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance.

We demonstrate the feasibility of integrating physics-based animations of solids and fluids with 3D Gaussian Splatting (3DGS) to create novel effects in virtual scenes reconstructed using 3DGS. Leveraging the coherence of the Gaussian splatting and position-based dynamics (PBD) in the underlying representation, we manage rendering, view synthesis, and the dynamics of solids and fluids in a cohesive manner. Similar to Gaussian shader, we enhance each Gaussian kernel with an added normal, aligning the kernel's orientation with the surface normal to refine the PBD simulation. This approach effectively eliminates spiky noises that arise from rotational deformation in solids. It also allows us to integrate physically based rendering to augment the dynamic surface reflections on fluids. Consequently, our framework is capable of realistically reproducing surface highlights on dynamic fluids and facilitating interactions between scene objects and fluids from new views. For more information, please visit our project page at https://amysteriouscat.github.io/GaussianSplashing/.

3D Gaussian Splatting (3DGS) achieves fast and high-quality renderings by using numerous small Gaussians, which leads to significant memory consumption. This reliance on a large number of Gaussians restricts the application of 3DGS-based models on low-cost devices due to memory limitations. However, simply reducing the number of Gaussians to accommodate devices with less memory capacity leads to inferior quality compared to the quality that can be achieved on high-end hardware. To address this lack of scalability, we propose integrating a Flexible Level of Detail (FLoD) to 3DGS, to allow a scene to be rendered at varying levels of detail according to hardware capabilities. While existing 3DGSs with LoD focus on detailed reconstruction, our method provides reconstructions using a small number of Gaussians for reduced memory requirements, and a larger number of Gaussians for greater detail. Experiments demonstrate our various rendering options with tradeoffs between rendering quality and memory usage, thereby allowing real-time rendering across different memory constraints. Furthermore, we show that our method generalizes to different 3DGS frameworks, indicating its potential for integration into future state-of-the-art developments. Project page: https://3dgs-flod.github.io/flod.github.io/

3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in novel view synthesis (NVS). However, 3DGS tends to overfit when trained with sparse views, limiting its generalization to novel viewpoints. In this paper, we address this overfitting issue by introducing Self-Ensembling Gaussian Splatting (SE-GS). We achieve self-ensembling by incorporating an uncertainty-aware perturbation strategy during training. A Delta-model and a Sigma-model are jointly trained on the available images. The Delta-model is dynamically perturbed based on rendering uncertainty across training steps, generating diverse perturbed models with negligible computational overhead. Discrepancies between the Sigma-model and these perturbed models are minimized throughout training, forming a robust ensemble of 3DGS models. This ensemble, represented by the Sigma-model, is then used to generate novel-view images during inference. Experimental results on the LLFF, Mip-NeRF360, DTU, and MVImgNet datasets demonstrate that our approach enhances NVS quality under few-shot training conditions, outperforming existing state-of-the-art methods. The code is released at: https://sailor-z.github.io/projects/SEGS.html.

We study the behavior of deterministic methods for solving inverse problems in imaging. These methods are commonly designed to achieve two goals: (1) attaining high perceptual quality, and (2) generating reconstructions that are consistent with the measurements. We provide a rigorous proof that the better a predictor satisfies these two requirements, the larger its Lipschitz constant must be, regardless of the nature of the degradation involved. In particular, to approach perfect perceptual quality and perfect consistency, the Lipschitz constant of the model must grow to infinity. This implies that such methods are necessarily more susceptible to adversarial attacks. We demonstrate our theory on single image super-resolution algorithms, addressing both noisy and noiseless settings. We also show how this undesired behavior can be leveraged to explore the posterior distribution, thereby allowing the deterministic model to imitate stochastic methods.

The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge over NeRF in terms of the training and inference speed, as well as the reconstruction quality. Although 3DGS works well for dense input images, the unstructured point-cloud like representation quickly overfits to the more challenging setup of extremely sparse input images (e.g., 3 images), creating a representation that appears as a jumble of needles from novel views. To address this issue, we propose regularized optimization and depth-based initialization. Our key idea is to introduce a structured Gaussian representation that can be controlled in 2D image space. We then constraint the Gaussians, in particular their position, and prevent them from moving independently during optimization. Specifically, we introduce single and multiview constraints through an implicit convolutional decoder and a total variation loss, respectively. With the coherency introduced to the Gaussians, we further constrain the optimization through a flow-based loss function. To support our regularized optimization, we propose an approach to initialize the Gaussians using monocular depth estimates at each input view. We demonstrate significant improvements compared to the state-of-the-art sparse-view NeRF-based approaches on a variety of scenes.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

In computer graphics, there is a need to recover easily modifiable representations of 3D geometry and appearance from image data. We introduce a novel method for this task using 3D Gaussian Splatting, which enables intuitive scene editing through mesh adjustments. Starting with input images and camera poses, we reconstruct the underlying geometry using a neural Signed Distance Field and extract a high-quality mesh. Our model then estimates a set of Gaussians, where each component is flat, and the opacity is conditioned on the recovered neural surface. To facilitate editing, we produce a proxy representation that encodes information about the Gaussians' shape and position. Unlike other methods, our pipeline allows modifications applied to the extracted mesh to be propagated to the proxy representation, from which we recover the updated parameters of the Gaussians. This effectively transfers the mesh edits back to the recovered appearance representation. By leveraging mesh-guided transformations, our approach simplifies 3D scene editing and offers improvements over existing methods in terms of usability and visual fidelity of edits. The complete source code for this project can be accessed at https://github.com/WJakubowska/NeuralSurfacePriors

4D Gaussian Splatting (4DGS) has recently gained considerable attention as a method for reconstructing dynamic scenes. Despite achieving superior quality, 4DGS typically requires substantial storage and suffers from slow rendering speed. In this work, we delve into these issues and identify two key sources of temporal redundancy. (Q1) Short-Lifespan Gaussians: 4DGS uses a large portion of Gaussians with short temporal span to represent scene dynamics, leading to an excessive number of Gaussians. (Q2) Inactive Gaussians: When rendering, only a small subset of Gaussians contributes to each frame. Despite this, all Gaussians are processed during rasterization, resulting in redundant computation overhead. To address these redundancies, we present 4DGS-1K, which runs at over 1000 FPS on modern GPUs. For Q1, we introduce the Spatial-Temporal Variation Score, a new pruning criterion that effectively removes short-lifespan Gaussians while encouraging 4DGS to capture scene dynamics using Gaussians with longer temporal spans. For Q2, we store a mask for active Gaussians across consecutive frames, significantly reducing redundant computations in rendering. Compared to vanilla 4DGS, our method achieves a 41times reduction in storage and 9times faster rasterization speed on complex dynamic scenes, while maintaining comparable visual quality. Please see our project page at https://4DGS-1K.github.io.

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations on top of a Gaussian noise distribution. We view the diffusion denoising process as a sequential decision making process, and show that it exhibits compounding errors similar to exposure bias issues in imitation learning problems. To mitigate these issues, we adapt the scheduled sampling algorithm to diffusion training. We conduct experiments on four markup datasets: mathematical formulas (LaTeX), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES). These experiments each verify the effectiveness of the diffusion process and the use of scheduled sampling to fix generation issues. These results also show that the markup-to-image task presents a useful controlled compositional setting for diagnosing and analyzing generative image models.

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit considerable performance degradation. By viewing the generation of diffusion models as a discretized integrating process, we argue that the quality drop is partly caused by applying an inaccurate integral direction to a timestep interval. To rectify this issue, we propose a timestep aligner that helps find a more accurate integral direction for a particular interval at the minimum cost. Specifically, at each denoising step, we replace the original parameterization by conditioning the network on a new timestep, which is obtained by aligning the sampling distribution to the real distribution. Extensive experiments show that our plug-in design can be trained efficiently and boost the inference performance of various state-of-the-art acceleration methods, especially when there are few denoising steps. For example, when using 10 denoising steps on the popular LSUN Bedroom dataset, we improve the FID of DDIM from 9.65 to 6.07, simply by adopting our method for a more appropriate set of timesteps. Code will be made publicly available.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness.

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called Type II maximum likelihood or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call Fully Bayesian Gaussian Process Regression (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Text-to-image generative models have made remarkable advancements in generating high-quality images. However, generated images often contain undesirable artifacts or other errors due to model limitations. Existing techniques to fine-tune generated images are time-consuming (manual editing), produce poorly-integrated results (inpainting), or result in unexpected changes across the entire image (variation selection and prompt fine-tuning). In this work, we present Diffusion Brush, a Latent Diffusion Model-based (LDM) tool to efficiently fine-tune desired regions within an AI-synthesized image. Our method introduces new random noise patterns at targeted regions during the reverse diffusion process, enabling the model to efficiently make changes to the specified regions while preserving the original context for the rest of the image. We evaluate our method's usability and effectiveness through a user study with artists, comparing our technique against other state-of-the-art image inpainting techniques and editing software for fine-tuning AI-generated imagery.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Low-light raw denoising is an important and valuable task in computational photography where learning-based methods trained with paired real data are mainstream. However, the limited data volume and complicated noise distribution have constituted a learnability bottleneck for paired real data, which limits the denoising performance of learning-based methods. To address this issue, we present a learnability enhancement strategy to reform paired real data according to noise modeling. Our strategy consists of two efficient techniques: shot noise augmentation (SNA) and dark shading correction (DSC). Through noise model decoupling, SNA improves the precision of data mapping by increasing the data volume and DSC reduces the complexity of data mapping by reducing the noise complexity. Extensive results on the public datasets and real imaging scenarios collectively demonstrate the state-of-the-art performance of our method. Our code is available at: https://github.com/megvii-research/PMN.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

Efficient text-to-image generation remains a challenging task due to the high computational costs associated with the multi-step sampling in diffusion models. Although distillation of pre-trained diffusion models has been successful in reducing sampling steps, low-step image generation often falls short in terms of quality. In this study, we propose a novel sampling design to achieve high-quality one-step image generation aligning with human preferences, particularly focusing on exploring the impact of the prior noise distribution. Our approach, Prompt Adaptive Human Preference Inversion (PAHI), optimizes the noise distributions for each prompt based on human preferences without the need for fine-tuning diffusion models. Our experiments showcase that the tailored noise distributions significantly improve image quality with only a marginal increase in computational cost. Our findings underscore the importance of noise optimization and pave the way for efficient and high-quality text-to-image synthesis.

There has been a recent surge of interest in modeling neural networks (NNs) as Gaussian processes. In the limit of a NN of infinite width the NN becomes equivalent to a Gaussian process. Here we demonstrate that for an ensemble of large, finite, fully connected networks with a single hidden layer the distribution of outputs at initialization is well described by a Gaussian perturbed by the fourth Hermite polynomial for weights drawn from a symmetric distribution. We show that the scale of the perturbation is inversely proportional to the number of units in the NN and that higher order terms decay more rapidly, thereby recovering the Edgeworth expansion. We conclude by observing that understanding how this perturbation changes under training would reveal the regimes in which the Gaussian process framework is valid to model NN behavior.

The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-output pairs with a PDE solver, train the neural network in the regression setting, and use the trained model as a cheap surrogate for the solver. The bottleneck in this scheme is the number of expensive queries of a PDE solver needed to generate the dataset. To alleviate the problem, we propose a computationally cheap augmentation strategy based on general covariance and simple random coordinate transformations. Our approach relies on the fact that physical laws are independent of the coordinate choice, so the change in the coordinate system preserves the type of a parametric PDE and only changes PDE's data (e.g., initial conditions, diffusion coefficient). For tried neural networks and partial differential equations, proposed augmentation improves test error by 23% on average. The worst observed result is a 17% increase in test error for multilayer perceptron, and the best case is a 80% decrease for dilated residual network.

Rendering dynamic scenes from monocular videos is a crucial yet challenging task. The recent deformable Gaussian Splatting has emerged as a robust solution to represent real-world dynamic scenes. However, it often leads to heavily redundant Gaussians, attempting to fit every training view at various time steps, leading to slower rendering speeds. Additionally, the attributes of Gaussians in static areas are time-invariant, making it unnecessary to model every Gaussian, which can cause jittering in static regions. In practice, the primary bottleneck in rendering speed for dynamic scenes is the number of Gaussians. In response, we introduce Efficient Dynamic Gaussian Splatting (EDGS), which represents dynamic scenes via sparse time-variant attribute modeling. Our approach formulates dynamic scenes using a sparse anchor-grid representation, with the motion flow of dense Gaussians calculated via a classical kernel representation. Furthermore, we propose an unsupervised strategy to efficiently filter out anchors corresponding to static areas. Only anchors associated with deformable objects are input into MLPs to query time-variant attributes. Experiments on two real-world datasets demonstrate that our EDGS significantly improves the rendering speed with superior rendering quality compared to previous state-of-the-art methods.

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

Conditioning image generation facilitates seamless editing and the creation of photorealistic images. However, conditioning on noisy or Out-of-Distribution (OoD) images poses significant challenges, particularly in balancing fidelity to the input and realism of the output. We introduce Confident Ordinary Differential Editing (CODE), a novel approach for image synthesis that effectively handles OoD guidance images. Utilizing a diffusion model as a generative prior, CODE enhances images through score-based updates along the probability-flow Ordinary Differential Equation (ODE) trajectory. This method requires no task-specific training, no handcrafted modules, and no assumptions regarding the corruptions affecting the conditioning image. Our method is compatible with any diffusion model. Positioned at the intersection of conditional image generation and blind image restoration, CODE operates in a fully blind manner, relying solely on a pre-trained generative model. Our method introduces an alternative approach to blind restoration: instead of targeting a specific ground truth image based on assumptions about the underlying corruption, CODE aims to increase the likelihood of the input image while maintaining fidelity. This results in the most probable in-distribution image around the input. Our contributions are twofold. First, CODE introduces a novel editing method based on ODE, providing enhanced control, realism, and fidelity compared to its SDE-based counterpart. Second, we introduce a confidence interval-based clipping method, which improves CODE's effectiveness by allowing it to disregard certain pixels or information, thus enhancing the restoration process in a blind manner. Experimental results demonstrate CODE's effectiveness over existing methods, particularly in scenarios involving severe degradation or OoD inputs.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.

Diffusion models have opened the path to a wide range of text-based image editing frameworks. However, these typically build on the multi-step nature of the diffusion backwards process, and adapting them to distilled, fast-sampling methods has proven surprisingly challenging. Here, we focus on a popular line of text-based editing frameworks - the ``edit-friendly'' DDPM-noise inversion approach. We analyze its application to fast sampling methods and categorize its failures into two classes: the appearance of visual artifacts, and insufficient editing strength. We trace the artifacts to mismatched noise statistics between inverted noises and the expected noise schedule, and suggest a shifted noise schedule which corrects for this offset. To increase editing strength, we propose a pseudo-guidance approach that efficiently increases the magnitude of edits without introducing new artifacts. All in all, our method enables text-based image editing with as few as three diffusion steps, while providing novel insights into the mechanisms behind popular text-based editing approaches.

Over the past few years, softmax and SGD have become a commonly used component and the default training strategy in CNN frameworks, respectively. However, when optimizing CNNs with SGD, the saturation behavior behind softmax always gives us an illusion of training well and then is omitted. In this paper, we first emphasize that the early saturation behavior of softmax will impede the exploration of SGD, which sometimes is a reason for model converging at a bad local-minima, then propose Noisy Softmax to mitigating this early saturation issue by injecting annealed noise in softmax during each iteration. This operation based on noise injection aims at postponing the early saturation and further bringing continuous gradients propagation so as to significantly encourage SGD solver to be more exploratory and help to find a better local-minima. This paper empirically verifies the superiority of the early softmax desaturation, and our method indeed improves the generalization ability of CNN model by regularization. We experimentally find that this early desaturation helps optimization in many tasks, yielding state-of-the-art or competitive results on several popular benchmark datasets.

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.

Large-scale vision foundation models such as DINOv2 boast impressive performances by leveraging massive architectures and training datasets. But numerous scenarios require practitioners to reproduce those pre-training solutions, such as on private data, new modalities, or simply for scientific questioning--which is currently extremely demanding computation-wise. We thus propose a novel pre-training strategy for DINOv2 that simultaneously accelerates convergence--and strengthens robustness to common corruptions as a by-product. Our approach involves a frequency filtering curriculum--low-frequency being seen first--and the Gaussian noise patching augmentation. Applied to a ViT-B/16 backbone trained on ImageNet-1K, while pre-training time and FLOPs are reduced by 1.6x and 2.25x, our method still achieves matching robustness in corruption benchmarks (ImageNet-C) and maintains competitive linear probing performance compared with baseline. This dual benefit of efficiency and robustness makes large-scale self-supervised foundation modeling more attainable, while opening the door to novel exploration around data curriculum and augmentation as means to improve self-supervised learning models robustness. The code is available at https://github.com/KevinZ0217/fast_dinov2

The pursuit of efficient and controllable high-quality content generation remains a central challenge in artificial intelligence-generated content (AIGC). While one-step generators, enabled by diffusion distillation techniques, offer excellent generation quality and computational efficiency, adapting them to new control conditions--such as structural constraints, semantic guidelines, or external inputs--poses a significant challenge. Conventional approaches often necessitate computationally expensive modifications to the base model and subsequent diffusion distillation. This paper introduces Noise Consistency Training (NCT), a novel and lightweight approach to directly integrate new control signals into pre-trained one-step generators without requiring access to original training images or retraining the base diffusion model. NCT operates by introducing an adapter module and employs a noise consistency loss in the noise space of the generator. This loss aligns the adapted model's generation behavior across noises that are conditionally dependent to varying degrees, implicitly guiding it to adhere to the new control. Theoretically, this training objective can be understood as minimizing the distributional distance between the adapted generator and the conditional distribution induced by the new conditions. NCT is modular, data-efficient, and easily deployable, relying only on the pre-trained one-step generator and a control signal model. Extensive experiments demonstrate that NCT achieves state-of-the-art controllable generation in a single forward pass, surpassing existing multi-step and distillation-based methods in both generation quality and computational efficiency. Code is available at https://github.com/Luo-Yihong/NCT

Style Transfer with Inference-Time Optimisation (ST-ITO) is a recent approach for transferring the applied effects of a reference audio to a raw audio track. It optimises the effect parameters to minimise the distance between the style embeddings of the processed audio and the reference. However, this method treats all possible configurations equally and relies solely on the embedding space, which can lead to unrealistic or biased results. We address this pitfall by introducing a Gaussian prior derived from a vocal preset dataset, DiffVox, over the parameter space. The resulting optimisation is equivalent to maximum-a-posteriori estimation. Evaluations on vocal effects transfer on the MedleyDB dataset show significant improvements across metrics compared to baselines, including a blind audio effects estimator, nearest-neighbour approaches, and uncalibrated ST-ITO. The proposed calibration reduces parameter mean squared error by up to 33% and matches the reference style better. Subjective evaluations with 16 participants confirm our method's superiority, especially in limited data regimes. This work demonstrates how incorporating prior knowledge in inference time enhances audio effects transfer, paving the way for more effective and realistic audio processing systems.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians $sum_{i=1}^k w_i N(mu_i,sigma^2), i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights w_i and the means \mu_i. We propose an algorithm that takes only 1{\varepsilon^{O(k)}} samples to estimate the weights w_i and the means \mu_i within \varepsilon$ error.

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of models. We develop theoretical guarantees for FA-LD for strongly log-concave distributions with non-i.i.d data and study how the injected noise and the stochastic-gradient noise, the heterogeneity of data, and the varying learning rates affect the convergence. Such an analysis sheds light on the optimal choice of local updates to minimize communication costs. Important to our approach is that the communication efficiency does not deteriorate with the injected noise in the Langevin algorithms. In addition, we examine in our FA-LD algorithm both independent and correlated noise used over different clients. We observe there is a trade-off between the pairs among communication, accuracy, and data privacy. As local devices may become inactive in federated networks, we also show convergence results based on different averaging schemes where only partial device updates are available. In such a case, we discover an additional bias that does not decay to zero.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Recently, 3D Gaussian splatting (3D-GS) has gained popularity in novel-view scene synthesis. It addresses the challenges of lengthy training times and slow rendering speeds associated with Neural Radiance Fields (NeRFs). Through rapid, differentiable rasterization of 3D Gaussians, 3D-GS achieves real-time rendering and accelerated training. They, however, demand substantial memory resources for both training and storage, as they require millions of Gaussians in their point cloud representation for each scene. We present a technique utilizing quantized embeddings to significantly reduce memory storage requirements and a coarse-to-fine training strategy for a faster and more stable optimization of the Gaussian point clouds. Our approach results in scene representations with fewer Gaussians and quantized representations, leading to faster training times and rendering speeds for real-time rendering of high resolution scenes. We reduce memory by more than an order of magnitude all while maintaining the reconstruction quality. We validate the effectiveness of our approach on a variety of datasets and scenes preserving the visual quality while consuming 10-20x less memory and faster training/inference speed. Project page and code is available https://efficientgaussian.github.io

Neural Radiance Fields (NeRFs) have demonstrated remarkable potential in capturing complex 3D scenes with high fidelity. However, one persistent challenge that hinders the widespread adoption of NeRFs is the computational bottleneck due to the volumetric rendering. On the other hand, 3D Gaussian splatting (3DGS) has recently emerged as an alternative representation that leverages a 3D Gaussisan-based representation and adopts the rasterization pipeline to render the images rather than volumetric rendering, achieving very fast rendering speed and promising image quality. However, a significant drawback arises as 3DGS entails a substantial number of 3D Gaussians to maintain the high fidelity of the rendered images, which requires a large amount of memory and storage. To address this critical issue, we place a specific emphasis on two key objectives: reducing the number of Gaussian points without sacrificing performance and compressing the Gaussian attributes, such as view-dependent color and covariance. To this end, we propose a learnable mask strategy that significantly reduces the number of Gaussians while preserving high performance. In addition, we propose a compact but effective representation of view-dependent color by employing a grid-based neural field rather than relying on spherical harmonics. Finally, we learn codebooks to compactly represent the geometric attributes of Gaussian by vector quantization. In our extensive experiments, we consistently show over 10times reduced storage and enhanced rendering speed, while maintaining the quality of the scene representation, compared to 3DGS. Our work provides a comprehensive framework for 3D scene representation, achieving high performance, fast training, compactness, and real-time rendering. Our project page is available at https://maincold2.github.io/c3dgs/.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

A primary challenge when deploying speaker recognition systems in real-world applications is performance degradation caused by environmental mismatch. We propose a diffusion-based method that takes speaker embeddings extracted from a pre-trained speaker recognition model and generates refined embeddings. For training, our approach progressively adds Gaussian noise to both clean and noisy speaker embeddings extracted from clean and noisy speech, respectively, via forward process of a diffusion model, and then reconstructs them to clean embeddings in the reverse process. While inferencing, all embeddings are regenerated via diffusion process. Our method needs neither speaker label nor any modification to the existing speaker recognition pipeline. Experiments on evaluation sets simulating environment mismatch scenarios show that our method can improve recognition accuracy by up to 19.6% over baseline models while retaining performance on conventional scenarios. We publish our code here https://github.com/kaistmm/seed-pytorch

Conventional uncertainty-aware temporal difference (TD) learning methods often rely on simplistic assumptions, typically including a zero-mean Gaussian distribution for TD errors. Such oversimplification can lead to inaccurate error representations and compromised uncertainty estimation. In this paper, we introduce a novel framework for generalized Gaussian error modeling in deep reinforcement learning, applicable to both discrete and continuous control settings. Our framework enhances the flexibility of error distribution modeling by incorporating additional higher-order moment, particularly kurtosis, thereby improving the estimation and mitigation of data-dependent noise, i.e., aleatoric uncertainty. We examine the influence of the shape parameter of the generalized Gaussian distribution (GGD) on aleatoric uncertainty and provide a closed-form expression that demonstrates an inverse relationship between uncertainty and the shape parameter. Additionally, we propose a theoretically grounded weighting scheme to fully leverage the GGD. To address epistemic uncertainty, we enhance the batch inverse variance weighting by incorporating bias reduction and kurtosis considerations, resulting in improved robustness. Extensive experimental evaluations using policy gradient algorithms demonstrate the consistent efficacy of our method, showcasing significant performance improvements.

We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. Noisy Student Training achieves 88.4% top-1 accuracy on ImageNet, which is 2.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 61.0% to 83.7%, reduces ImageNet-C mean corruption error from 45.7 to 28.3, and reduces ImageNet-P mean flip rate from 27.8 to 12.2. Noisy Student Training extends the idea of self-training and distillation with the use of equal-or-larger student models and noise added to the student during learning. On ImageNet, we first train an EfficientNet model on labeled images and use it as a teacher to generate pseudo labels for 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the learning of the student, we inject noise such as dropout, stochastic depth, and data augmentation via RandAugment to the student so that the student generalizes better than the teacher. Models are available at https://github.com/tensorflow/tpu/tree/master/models/official/efficientnet. Code is available at https://github.com/google-research/noisystudent.

This study introduces a novel and interpretable model, DiffVox, for matching vocal effects in music production. DiffVox, short for ``Differentiable Vocal Fx", integrates parametric equalisation, dynamic range control, delay, and reverb with efficient differentiable implementations to enable gradient-based optimisation for parameter estimation. Vocal presets are retrieved from two datasets, comprising 70 tracks from MedleyDB and 365 tracks from a private collection. Analysis of parameter correlations highlights strong relationships between effects and parameters, such as the high-pass and low-shelf filters often behaving together to shape the low end, and the delay time correlates with the intensity of the delayed signals. Principal component analysis reveals connections to McAdams' timbre dimensions, where the most crucial component modulates the perceived spaciousness while the secondary components influence spectral brightness. Statistical testing confirms the non-Gaussian nature of the parameter distribution, highlighting the complexity of the vocal effects space. These initial findings on the parameter distributions set the foundation for future research in vocal effects modelling and automatic mixing. Our source code and datasets are accessible at https://github.com/SonyResearch/diffvox.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

The modeling and manipulation of 3D scenes captured from the real world are pivotal in various applications, attracting growing research interest. While previous works on editing have achieved interesting results through manipulating 3D meshes, they often require accurately reconstructed meshes to perform editing, which limits their application in 3D content generation. To address this gap, we introduce a novel single-image-driven 3D scene editing approach based on 3D Gaussian Splatting, enabling intuitive manipulation via directly editing the content on a 2D image plane. Our method learns to optimize the 3D Gaussians to align with an edited version of the image rendered from a user-specified viewpoint of the original scene. To capture long-range object deformation, we introduce positional loss into the optimization process of 3D Gaussian Splatting and enable gradient propagation through reparameterization. To handle occluded 3D Gaussians when rendering from the specified viewpoint, we build an anchor-based structure and employ a coarse-to-fine optimization strategy capable of handling long-range deformation while maintaining structural stability. Furthermore, we design a novel masking strategy to adaptively identify non-rigid deformation regions for fine-scale modeling. Extensive experiments show the effectiveness of our method in handling geometric details, long-range, and non-rigid deformation, demonstrating superior editing flexibility and quality compared to previous approaches.

The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the Unscented Transform (UT) -- a well-known distribution approximation used in the Unscented Kalman Filter (UKF) from the field of filtering. A finite set of statistics called sigma points, sampled deterministically, provides a more informative and lower-variance posterior representation than the ubiquitous noise-scaling of the reparameterization trick, while ensuring higher-quality reconstruction. We further boost the performance by replacing the Kullback-Leibler (KL) divergence with the Wasserstein distribution metric that allows for a sharper posterior. Inspired by the two components, we derive a novel, deterministic-sampling flavor of the VAE, the Unscented Autoencoder (UAE), trained purely with regularization-like terms on the per-sample posterior. We empirically show competitive performance in Fr\'echet Inception Distance (FID) scores over closely-related models, in addition to a lower training variance than the VAE.

Masked generative models (MGMs) have shown impressive generative ability while providing an order of magnitude efficient sampling steps compared to continuous diffusion models. However, MGMs still underperform in image synthesis compared to recent well-developed continuous diffusion models with similar size in terms of quality and diversity of generated samples. A key factor in the performance of continuous diffusion models stems from the guidance methods, which enhance the sample quality at the expense of diversity. In this paper, we extend these guidance methods to generalized guidance formulation for MGMs and propose a self-guidance sampling method, which leads to better generation quality. The proposed approach leverages an auxiliary task for semantic smoothing in vector-quantized token space, analogous to the Gaussian blur in continuous pixel space. Equipped with the parameter-efficient fine-tuning method and high-temperature sampling, MGMs with the proposed self-guidance achieve a superior quality-diversity trade-off, outperforming existing sampling methods in MGMs with more efficient training and sampling costs. Extensive experiments with the various sampling hyperparameters confirm the effectiveness of the proposed self-guidance.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

We introduce Gaussian-Flow, a novel point-based approach for fast dynamic scene reconstruction and real-time rendering from both multi-view and monocular videos. In contrast to the prevalent NeRF-based approaches hampered by slow training and rendering speeds, our approach harnesses recent advancements in point-based 3D Gaussian Splatting (3DGS). Specifically, a novel Dual-Domain Deformation Model (DDDM) is proposed to explicitly model attribute deformations of each Gaussian point, where the time-dependent residual of each attribute is captured by a polynomial fitting in the time domain, and a Fourier series fitting in the frequency domain. The proposed DDDM is capable of modeling complex scene deformations across long video footage, eliminating the need for training separate 3DGS for each frame or introducing an additional implicit neural field to model 3D dynamics. Moreover, the explicit deformation modeling for discretized Gaussian points ensures ultra-fast training and rendering of a 4D scene, which is comparable to the original 3DGS designed for static 3D reconstruction. Our proposed approach showcases a substantial efficiency improvement, achieving a 5times faster training speed compared to the per-frame 3DGS modeling. In addition, quantitative results demonstrate that the proposed Gaussian-Flow significantly outperforms previous leading methods in novel view rendering quality. Project page: https://nju-3dv.github.io/projects/Gaussian-Flow

We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls. In our setup, the client must encode the rewards such that the second moment of the encoded rewards is no more than P, and this encoded reward is further corrupted by additive Gaussian noise of variance sigma^2; the learner only has access to this corrupted reward. For this setting, we derive an information-theoretic lower bound of Omegaleft(frac{KT{SNR wedge1}} right) on the minimax regret of any scheme, where SNR := P{sigma^2}, and K and T are the number of arms and time horizon, respectively. Furthermore, we propose a multi-phase bandit algorithm, UEtext{-UCB++}, which matches this lower bound to a minor additive factor. UEtext{-UCB++} performs uniform exploration in its initial phases and then utilizes the {\em upper confidence bound }(UCB) bandit algorithm in its final phase. An interesting feature of UEtext{-UCB++} is that the coarser estimates of the mean rewards formed during a uniform exploration phase help to refine the encoding protocol in the next phase, leading to more accurate mean estimates of the rewards in the subsequent phase. This positive reinforcement cycle is critical to reducing the number of uniform exploration rounds and closely matching our lower bound.

We propose a simple but effective training-free approach tailored to diffusion-based image-to-image translation. Our approach revises the original noise prediction network of a pretrained diffusion model by introducing a noise correction term. We formulate the noise correction term as the difference between two noise predictions; one is computed from the denoising network with a progressive interpolation of the source and target prompt embeddings, while the other is the noise prediction with the source prompt embedding. The final noise prediction network is given by a linear combination of the standard denoising term and the noise correction term, where the former is designed to reconstruct must-be-preserved regions while the latter aims to effectively edit regions of interest relevant to the target prompt. Our approach can be easily incorporated into existing image-to-image translation methods based on diffusion models. Extensive experiments verify that the proposed technique achieves outstanding performance with low latency and consistently improves existing frameworks when combined with them.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector (SMV) case to the temporally correlated multiple measurement vector (MMV) case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

3D Gaussian Splatting (3DGS) has made significant strides in novel view synthesis but is limited by the substantial number of Gaussian primitives required, posing challenges for deployment on lightweight devices. Recent methods address this issue by compressing the storage size of densified Gaussians, yet fail to preserve rendering quality and efficiency. To overcome these limitations, we propose ProtoGS to learn Gaussian prototypes to represent Gaussian primitives, significantly reducing the total Gaussian amount without sacrificing visual quality. Our method directly uses Gaussian prototypes to enable efficient rendering and leverage the resulting reconstruction loss to guide prototype learning. To further optimize memory efficiency during training, we incorporate structure-from-motion (SfM) points as anchor points to group Gaussian primitives. Gaussian prototypes are derived within each group by clustering of K-means, and both the anchor points and the prototypes are optimized jointly. Our experiments on real-world and synthetic datasets prove that we outperform existing methods, achieving a substantial reduction in the number of Gaussians, and enabling high rendering speed while maintaining or even enhancing rendering fidelity.

Aligning diffusion models to downstream tasks often requires finetuning new models or gradient-based guidance at inference time to enable sampling from the reward-tilted posterior. In this work, we explore a simple inference-time gradient-free guidance approach, called controlled denoising (CoDe), that circumvents the need for differentiable guidance functions and model finetuning. CoDe is a blockwise sampling method applied during intermediate denoising steps, allowing for alignment with downstream rewards. Our experiments demonstrate that, despite its simplicity, CoDe offers a favorable trade-off between reward alignment, prompt instruction following, and inference cost, achieving a competitive performance against the state-of-the-art baselines. Our code is available at: https://github.com/anujinho/code.

Neural Radiance Fields (NeRFs) have demonstrated the remarkable potential of neural networks to capture the intricacies of 3D objects. By encoding the shape and color information within neural network weights, NeRFs excel at producing strikingly sharp novel views of 3D objects. Recently, numerous generalizations of NeRFs utilizing generative models have emerged, expanding its versatility. In contrast, Gaussian Splatting (GS) offers a similar render quality with faster training and inference as it does not need neural networks to work. It encodes information about the 3D objects in the set of Gaussian distributions that can be rendered in 3D similarly to classical meshes. Unfortunately, GS are difficult to condition since they usually require circa hundred thousand Gaussian components. To mitigate the caveats of both models, we propose a hybrid model Viewing Direction Gaussian Splatting (VDGS) that uses GS representation of the 3D object's shape and NeRF-based encoding of color and opacity. Our model uses Gaussian distributions with trainable positions (i.e. means of Gaussian), shape (i.e. covariance of Gaussian), color and opacity, and a neural network that takes Gaussian parameters and viewing direction to produce changes in the said color and opacity. As a result, our model better describes shadows, light reflections, and the transparency of 3D objects without adding additional texture and light components.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

In this paper, we present an embarrassingly simple yet effective solution to a seemingly impossible mission, low-light image enhancement (LLIE) without access to any task-related data. The proposed solution, Noise SElf-Regression (NoiSER), simply learns a convolutional neural network equipped with a instance-normalization layer by taking a random noise image, N(0,sigma^2) for each pixel, as both input and output for each training pair, and then the low-light image is fed to the learned network for predicting the normal-light image. Technically, an intuitive explanation for its effectiveness is as follows: 1) the self-regression reconstructs the contrast between adjacent pixels of the input image, 2) the instance-normalization layers may naturally remediate the overall magnitude/lighting of the input image, and 3) the N(0,sigma^2) assumption for each pixel enforces the output image to follow the well-known gray-world hypothesis Gary-world_Hypothesis when the image size is big enough, namely, the averages of three RGB components of an image converge to the same value. Compared to existing SOTA LLIE methods with access to different task-related data, NoiSER is surprisingly highly competitive in enhancement quality, yet with a much smaller model size, and much lower training and inference cost. With only sim 1K parameters, NoiSER realizes about 1 minute for training and 1.2 ms for inference with 600x400 resolution on RTX 2080 Ti. As a bonus, NoiSER possesses automated over-exposure suppression ability and shows excellent performance on over-exposed photos.

Diffusion probabilistic models have been shown to generate state-of-the-art results on several competitive image synthesis benchmarks but lack a low-dimensional, interpretable latent space, and are slow at generation. On the other hand, standard Variational Autoencoders (VAEs) typically have access to a low-dimensional latent space but exhibit poor sample quality. We present DiffuseVAE, a novel generative framework that integrates VAE within a diffusion model framework, and leverage this to design novel conditional parameterizations for diffusion models. We show that the resulting model equips diffusion models with a low-dimensional VAE inferred latent code which can be used for downstream tasks like controllable synthesis. The proposed method also improves upon the speed vs quality tradeoff exhibited in standard unconditional DDPM/DDIM models (for instance, FID of 16.47 vs 34.36 using a standard DDIM on the CelebA-HQ-128 benchmark using T=10 reverse process steps) without having explicitly trained for such an objective. Furthermore, the proposed model exhibits synthesis quality comparable to state-of-the-art models on standard image synthesis benchmarks like CIFAR-10 and CelebA-64 while outperforming most existing VAE-based methods. Lastly, we show that the proposed method exhibits inherent generalization to different types of noise in the conditioning signal. For reproducibility, our source code is publicly available at https://github.com/kpandey008/DiffuseVAE.

3D Gaussian Splatting (3DGS) has become an emerging technique with remarkable potential in 3D representation and image rendering. However, the substantial storage overhead of 3DGS significantly impedes its practical applications. In this work, we formulate the compact 3D Gaussian learning as an end-to-end Rate-Distortion Optimization (RDO) problem and propose RDO-Gaussian that can achieve flexible and continuous rate control. RDO-Gaussian addresses two main issues that exist in current schemes: 1) Different from prior endeavors that minimize the rate under the fixed distortion, we introduce dynamic pruning and entropy-constrained vector quantization (ECVQ) that optimize the rate and distortion at the same time. 2) Previous works treat the colors of each Gaussian equally, while we model the colors of different regions and materials with learnable numbers of parameters. We verify our method on both real and synthetic scenes, showcasing that RDO-Gaussian greatly reduces the size of 3D Gaussian over 40x, and surpasses existing methods in rate-distortion performance.

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

With the availability of large-scale video datasets and the advances of diffusion models, text-driven video generation has achieved substantial progress. However, existing video generation models are typically trained on a limited number of frames, resulting in the inability to generate high-fidelity long videos during inference. Furthermore, these models only support single-text conditions, whereas real-life scenarios often require multi-text conditions as the video content changes over time. To tackle these challenges, this study explores the potential of extending the text-driven capability to generate longer videos conditioned on multiple texts. 1) We first analyze the impact of initial noise in video diffusion models. Then building upon the observation of noise, we propose FreeNoise, a tuning-free and time-efficient paradigm to enhance the generative capabilities of pretrained video diffusion models while preserving content consistency. Specifically, instead of initializing noises for all frames, we reschedule a sequence of noises for long-range correlation and perform temporal attention over them by window-based function. 2) Additionally, we design a novel motion injection method to support the generation of videos conditioned on multiple text prompts. Extensive experiments validate the superiority of our paradigm in extending the generative capabilities of video diffusion models. It is noteworthy that compared with the previous best-performing method which brought about 255% extra time cost, our method incurs only negligible time cost of approximately 17%. Generated video samples are available at our website: http://haonanqiu.com/projects/FreeNoise.html.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame occurrence times (or indices) into RGB color values. Although INRs facilitate effective compression, they are unsuitable for editing purposes. One potential solution is to use a 3D Gaussian Splatting (3DGS) based model, such as the Video Gaussian Representation (VGR), which is capable of encoding video as a multitude of 3D Gaussians and is applicable for numerous video processing operations, including editing. Nevertheless, in this case, the capacity for modification is constrained to a limited set of basic transformations. To address this issue, we introduce the Video Gaussian Splatting (VeGaS) model, which enables realistic modifications of video data. To construct VeGaS, we propose a novel family of Folded-Gaussian distributions designed to capture nonlinear dynamics in a video stream and model consecutive frames by 2D Gaussians obtained as respective conditional distributions. Our experiments demonstrate that VeGaS outperforms state-of-the-art solutions in frame reconstruction tasks and allows realistic modifications of video data. The code is available at: https://github.com/gmum/VeGaS.

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In this work, we demonstrate that NFs are more powerful than previously believed. We present TarFlow: a simple and scalable architecture that enables highly performant NF models. TarFlow can be thought of as a Transformer-based variant of Masked Autoregressive Flows (MAFs): it consists of a stack of autoregressive Transformer blocks on image patches, alternating the autoregression direction between layers. TarFlow is straightforward to train end-to-end, and capable of directly modeling and generating pixels. We also propose three key techniques to improve sample quality: Gaussian noise augmentation during training, a post training denoising procedure, and an effective guidance method for both class-conditional and unconditional settings. Putting these together, TarFlow sets new state-of-the-art results on likelihood estimation for images, beating the previous best methods by a large margin, and generates samples with quality and diversity comparable to diffusion models, for the first time with a stand-alone NF model. We make our code available at https://github.com/apple/ml-tarflow.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

The recent Gaussian Splatting achieves high-quality and real-time novel-view synthesis of the 3D scenes. However, it is solely concentrated on the appearance and geometry modeling, while lacking in fine-grained object-level scene understanding. To address this issue, we propose Gaussian Grouping, which extends Gaussian Splatting to jointly reconstruct and segment anything in open-world 3D scenes. We augment each Gaussian with a compact Identity Encoding, allowing the Gaussians to be grouped according to their object instance or stuff membership in the 3D scene. Instead of resorting to expensive 3D labels, we supervise the Identity Encodings during the differentiable rendering by leveraging the 2D mask predictions by SAM, along with introduced 3D spatial consistency regularization. Comparing to the implicit NeRF representation, we show that the discrete and grouped 3D Gaussians can reconstruct, segment and edit anything in 3D with high visual quality, fine granularity and efficiency. Based on Gaussian Grouping, we further propose a local Gaussian Editing scheme, which shows efficacy in versatile scene editing applications, including 3D object removal, inpainting, colorization and scene recomposition. Our code and models will be at https://github.com/lkeab/gaussian-grouping.

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems. For example, we achieve a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of 9.12dB compared to existing methods.

Anchor-based 3D Gaussian splatting (3D-GS) exploits anchor features in 3D Gaussian prediction, which has achieved impressive 3D rendering quality with reduced Gaussian redundancy. On the other hand, it often encounters the dilemma among anchor features, model size, and rendering quality - large anchor features lead to large 3D models and high-quality rendering whereas reducing anchor features degrades Gaussian attribute prediction which leads to clear artifacts in the rendered textures and geometries. We design SOGS, an anchor-based 3D-GS technique that introduces second-order anchors to achieve superior rendering quality and reduced anchor features and model size simultaneously. Specifically, SOGS incorporates covariance-based second-order statistics and correlation across feature dimensions to augment features within each anchor, compensating for the reduced feature size and improving rendering quality effectively. In addition, it introduces a selective gradient loss to enhance the optimization of scene textures and scene geometries, leading to high-quality rendering with small anchor features. Extensive experiments over multiple widely adopted benchmarks show that SOGS achieves superior rendering quality in novel view synthesis with clearly reduced model size.

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple modifications to DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.