import math import torch import torch.nn.functional as F from torch import nn from einops import reduce from tqdm.auto import tqdm from functools import partial from .transformer import Transformer from .model_utils import default, identity, extract # gaussian diffusion trainer class def linear_beta_schedule(timesteps): scale = 1000 / timesteps beta_start = scale * 0.0001 beta_end = scale * 0.02 return torch.linspace(beta_start, beta_end, timesteps, dtype=torch.float64) def cosine_beta_schedule(timesteps, s=0.008): """ cosine schedule as proposed in https://openreview.net/forum?id=-NEXDKk8gZ """ steps = timesteps + 1 x = torch.linspace(0, timesteps, steps, dtype=torch.float64) alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2 alphas_cumprod = alphas_cumprod / alphas_cumprod[0] betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1]) return torch.clip(betas, 0, 0.999) class Diffusion_TS(nn.Module): def __init__( self, seq_length, feature_size, n_layer_enc=3, n_layer_dec=6, d_model=None, timesteps=1000, sampling_timesteps=None, loss_type="l1", beta_schedule="cosine", n_heads=4, mlp_hidden_times=4, eta=0.0, attn_pd=0.0, resid_pd=0.0, kernel_size=None, padding_size=None, use_ff=True, reg_weight=None, **kwargs, ): super(Diffusion_TS, self).__init__() self.eta, self.use_ff = eta, use_ff self.seq_length = seq_length self.feature_size = feature_size self.ff_weight = default(reg_weight, math.sqrt(self.seq_length) / 5) self.model = Transformer( n_feat=feature_size, n_channel=seq_length, n_layer_enc=n_layer_enc, n_layer_dec=n_layer_dec, n_heads=n_heads, attn_pdrop=attn_pd, resid_pdrop=resid_pd, mlp_hidden_times=mlp_hidden_times, max_len=seq_length, n_embd=d_model, conv_params=[kernel_size, padding_size], **kwargs, ) if beta_schedule == "linear": betas = linear_beta_schedule(timesteps) elif beta_schedule == "cosine": betas = cosine_beta_schedule(timesteps) else: raise ValueError(f"unknown beta schedule {beta_schedule}") alphas = 1.0 - betas alphas_cumprod = torch.cumprod(alphas, dim=0) alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value=1.0) (timesteps,) = betas.shape self.num_timesteps = int(timesteps) self.loss_type = loss_type # sampling related parameters self.sampling_timesteps = default( sampling_timesteps, timesteps ) # default num sampling timesteps to number of timesteps at training assert self.sampling_timesteps <= timesteps self.fast_sampling = self.sampling_timesteps < timesteps # helper function to register buffer from float64 to float32 register_buffer = lambda name, val: self.register_buffer( name, val.to(torch.float32) ) register_buffer("betas", betas) register_buffer("alphas_cumprod", alphas_cumprod) register_buffer("alphas_cumprod_prev", alphas_cumprod_prev) # calculations for diffusion q(x_t | x_{t-1}) and others register_buffer("sqrt_alphas_cumprod", torch.sqrt(alphas_cumprod)) register_buffer( "sqrt_one_minus_alphas_cumprod", torch.sqrt(1.0 - alphas_cumprod) ) register_buffer("log_one_minus_alphas_cumprod", torch.log(1.0 - alphas_cumprod)) register_buffer("sqrt_recip_alphas_cumprod", torch.sqrt(1.0 / alphas_cumprod)) register_buffer( "sqrt_recipm1_alphas_cumprod", torch.sqrt(1.0 / alphas_cumprod - 1) ) # calculations for posterior q(x_{t-1} | x_t, x_0) posterior_variance = ( betas * (1.0 - alphas_cumprod_prev) / (1.0 - alphas_cumprod) ) # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t) register_buffer("posterior_variance", posterior_variance) # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain register_buffer( "posterior_log_variance_clipped", torch.log(posterior_variance.clamp(min=1e-20)), ) register_buffer( "posterior_mean_coef1", betas * torch.sqrt(alphas_cumprod_prev) / (1.0 - alphas_cumprod), ) register_buffer( "posterior_mean_coef2", (1.0 - alphas_cumprod_prev) * torch.sqrt(alphas) / (1.0 - alphas_cumprod), ) # calculate reweighting register_buffer( "loss_weight", torch.sqrt(alphas) * torch.sqrt(1.0 - alphas_cumprod) / betas / 100, ) def predict_noise_from_start(self, x_t, t, x0): return ( extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x0 ) / extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) def predict_start_from_noise(self, x_t, t, noise): return ( extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise ) def q_posterior(self, x_start, x_t, t): posterior_mean = ( extract(self.posterior_mean_coef1, t, x_t.shape) * x_start + extract(self.posterior_mean_coef2, t, x_t.shape) * x_t ) posterior_variance = extract(self.posterior_variance, t, x_t.shape) posterior_log_variance_clipped = extract( self.posterior_log_variance_clipped, t, x_t.shape ) return posterior_mean, posterior_variance, posterior_log_variance_clipped def output(self, x, t, padding_masks=None): trend, season = self.model(x, t, padding_masks=padding_masks) model_output = trend + season return model_output def model_predictions(self, x, t, clip_x_start=False, padding_masks=None): if padding_masks is None: padding_masks = torch.ones( x.shape[0], self.seq_length, dtype=bool, device=x.device ) maybe_clip = ( partial(torch.clamp, min=-1.0, max=1.0) if clip_x_start else identity ) x_start = self.output(x, t, padding_masks) x_start = maybe_clip(x_start) pred_noise = self.predict_noise_from_start(x, t, x_start) return pred_noise, x_start def p_mean_variance(self, x, t, clip_denoised=True): _, x_start = self.model_predictions(x, t) if clip_denoised: x_start.clamp_(-1.0, 1.0) model_mean, posterior_variance, posterior_log_variance = self.q_posterior( x_start=x_start, x_t=x, t=t ) return model_mean, posterior_variance, posterior_log_variance, x_start def p_sample(self, x, t: int, clip_denoised=True): batched_times = torch.full((x.shape[0],), t, device=x.device, dtype=torch.long) model_mean, _, model_log_variance, x_start = self.p_mean_variance( x=x, t=batched_times, clip_denoised=clip_denoised ) noise = torch.randn_like(x) if t > 0 else 0.0 # no noise if t == 0 pred_img = model_mean + (0.5 * model_log_variance).exp() * noise return pred_img, x_start @torch.no_grad() def sample(self, shape): device = self.betas.device img = torch.randn(shape, device=device) for t in tqdm( reversed(range(0, self.num_timesteps)), desc="sampling loop time step", total=self.num_timesteps, ): img, _ = self.p_sample(img, t) return img @torch.no_grad() def fast_sample(self, shape, clip_denoised=True): batch, device, total_timesteps, sampling_timesteps, eta = ( shape[0], self.betas.device, self.num_timesteps, self.sampling_timesteps, self.eta, ) # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1) times = list(reversed(times.int().tolist())) time_pairs = list( zip(times[:-1], times[1:]) ) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)] img = torch.randn(shape, device=device) for time, time_next in tqdm(time_pairs, desc="sampling loop time step"): time_cond = torch.full((batch,), time, device=device, dtype=torch.long) pred_noise, x_start, *_ = self.model_predictions( img, time_cond, clip_x_start=clip_denoised ) if time_next < 0: img = x_start continue alpha = self.alphas_cumprod[time] alpha_next = self.alphas_cumprod[time_next] sigma = ( eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt() ) c = (1 - alpha_next - sigma**2).sqrt() noise = torch.randn_like(img) img = x_start * alpha_next.sqrt() + c * pred_noise + sigma * noise return img def generate_mts(self, batch_size=16): feature_size, seq_length = self.feature_size, self.seq_length sample_fn = self.fast_sample if self.fast_sampling else self.sample return sample_fn((batch_size, seq_length, feature_size)) @property def loss_fn(self): if self.loss_type == "l1": return F.l1_loss elif self.loss_type == "l2": return F.mse_loss else: raise ValueError(f"invalid loss type {self.loss_type}") def q_sample(self, x_start, t, noise=None): noise = default(noise, lambda: torch.randn_like(x_start)) return ( extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start + extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise ) def _train_loss(self, x_start, t, target=None, noise=None, padding_masks=None): noise = default(noise, lambda: torch.randn_like(x_start)) if target is None: target = x_start x = self.q_sample(x_start=x_start, t=t, noise=noise) # noise sample model_out = self.output(x, t, padding_masks) train_loss = self.loss_fn(model_out, target, reduction="none") fourier_loss = torch.tensor([0.0]) if self.use_ff: fft1 = torch.fft.fft(model_out.transpose(1, 2), norm="forward") fft2 = torch.fft.fft(target.transpose(1, 2), norm="forward") fft1, fft2 = fft1.transpose(1, 2), fft2.transpose(1, 2) fourier_loss = self.loss_fn( torch.real(fft1), torch.real(fft2), reduction="none" ) + self.loss_fn(torch.imag(fft1), torch.imag(fft2), reduction="none") train_loss += self.ff_weight * fourier_loss train_loss = reduce(train_loss, "b ... -> b (...)", "mean") train_loss = train_loss * extract(self.loss_weight, t, train_loss.shape) return train_loss.mean() def forward(self, x, **kwargs): ( b, c, n, device, feature_size, ) = ( *x.shape, x.device, self.feature_size, ) assert n == feature_size, f"number of variable must be {feature_size}" t = torch.randint(0, self.num_timesteps, (b,), device=device).long() return self._train_loss(x_start=x, t=t, **kwargs) def return_components(self, x, t: int): ( b, c, n, device, feature_size, ) = ( *x.shape, x.device, self.feature_size, ) assert n == feature_size, f"number of variable must be {feature_size}" t = torch.tensor([t]) t = t.repeat(b).to(device) x = self.q_sample(x, t) trend, season, residual = self.model(x, t, return_res=True) return trend, season, residual, x def fast_sample_infill( self, shape, target, sampling_timesteps, partial_mask=None, clip_denoised=True, model_kwargs=None, ): batch, device, total_timesteps, eta = ( shape[0], self.betas.device, self.num_timesteps, self.eta, ) # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1) times = list(reversed(times.int().tolist())) time_pairs = list( zip(times[:-1], times[1:]) ) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)] img = torch.randn(shape, device=device) for time, time_next in tqdm( time_pairs, desc="conditional sampling loop time step" ): time_cond = torch.full((batch,), time, device=device, dtype=torch.long) pred_noise, x_start, *_ = self.model_predictions( img, time_cond, clip_x_start=clip_denoised ) if time_next < 0: img = x_start continue alpha = self.alphas_cumprod[time] alpha_next = self.alphas_cumprod[time_next] sigma = ( eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt() ) c = (1 - alpha_next - sigma**2).sqrt() pred_mean = x_start * alpha_next.sqrt() + c * pred_noise noise = torch.randn_like(img) img = pred_mean + sigma * noise img = self.langevin_fn( sample=img, mean=pred_mean, sigma=sigma, t=time_cond, tgt_embs=target, partial_mask=partial_mask, **model_kwargs, ) target_t = self.q_sample(target, t=time_cond) img[partial_mask] = target_t[partial_mask] img[partial_mask] = target[partial_mask] return img def sample_infill( self, shape, target, partial_mask=None, clip_denoised=True, model_kwargs=None, ): """ Generate samples from the model and yield intermediate samples from each timestep of diffusion. """ batch, device = shape[0], self.betas.device img = torch.randn(shape, device=device) for t in tqdm( reversed(range(0, self.num_timesteps)), desc="conditional sampling loop time step", total=self.num_timesteps, ): img = self.p_sample_infill( x=img, t=t, clip_denoised=clip_denoised, target=target, partial_mask=partial_mask, model_kwargs=model_kwargs, ) img[partial_mask] = target[partial_mask] return img def p_sample_infill( self, x, target, t: int, partial_mask=None, clip_denoised=True, model_kwargs=None, ): b, *_, device = *x.shape, self.betas.device batched_times = torch.full((x.shape[0],), t, device=x.device, dtype=torch.long) model_mean, _, model_log_variance, _ = self.p_mean_variance( x=x, t=batched_times, clip_denoised=clip_denoised ) noise = torch.randn_like(x) if t > 0 else 0.0 # no noise if t == 0 sigma = (0.5 * model_log_variance).exp() pred_img = model_mean + sigma * noise pred_img = self.langevin_fn( sample=pred_img, mean=model_mean, sigma=sigma, t=batched_times, tgt_embs=target, partial_mask=partial_mask, **model_kwargs, ) print(sigma.mean()) target_t = self.q_sample(target, t=batched_times) pred_img[partial_mask] = target_t[partial_mask] return pred_img def langevin_fn( self, coef, partial_mask, tgt_embs, learning_rate, sample, mean, sigma, t, coef_=0.0, **kwargs, ): # we thus run more gradient updates at large diffusion step t to guide the generation then # reduce the number of gradient steps in stages to accelerate sampling. if t[0].item() < self.num_timesteps * 0.05: K = 0 elif t[0].item() > self.num_timesteps * 0.9: K = 3 elif t[0].item() > self.num_timesteps * 0.75: K = 2 learning_rate = learning_rate * 0.5 else: K = 1 learning_rate = learning_rate * 0.25 input_embs_param = torch.nn.Parameter(sample) with torch.enable_grad(): for i in range(K): optimizer = torch.optim.Adagrad([input_embs_param], lr=learning_rate) optimizer.zero_grad() x_start = self.output(x=input_embs_param, t=t) if sigma.mean() == 0: logp_term = ( coef * ((mean - input_embs_param) ** 2 / 1.0).mean(dim=0).sum() ) infill_loss = (x_start[partial_mask] - tgt_embs[partial_mask]) ** 2 infill_loss = infill_loss.mean(dim=0).sum() else: logp_term = ( coef * ((mean - input_embs_param) ** 2 / sigma).mean(dim=0).sum() ) infill_loss = (x_start[partial_mask] - tgt_embs[partial_mask]) ** 2 infill_loss = (infill_loss / sigma.mean()).mean(dim=0).sum() # 第二个等号后面最后一项消失了，因为当我们要求模型生成“狗”的图像时，扩散过程始终 # 不变，对应的梯度也是0，可以抹掉。 # https://lichtung612.github.io/posts/3-diffusion-models/ # 第三个等号后面两项中，第一项是扩散模型本身的梯度引导，新增的只能是第二项，即classifier guidance只需要额外添加一个classifier的梯度来引导。 if "auc_threshold" in kwargs: auc_threshold = kwargs.get("auc_threshold") auc_loss = compute_auc_loss( input_embs_param, tgt_embs, auc_threshold ) * (5 - K) else: auc_loss = 0 loss = logp_term + infill_loss + auc_loss print(logp_term, infill_loss, auc_loss) loss.backward() optimizer.step() # add more noise epsilon = torch.randn_like(input_embs_param.data) input_embs_param = torch.nn.Parameter( ( input_embs_param.data + coef_ * sigma.mean().item() * epsilon ).detach() ) sample[~partial_mask] = input_embs_param.data[~partial_mask] return sample import torch.nn.functional as F def compute_auc_loss(predictions: torch.Tensor, targets=None, auc_threshold=None): # with torch.no_grad(): # if not auc_threshold: # auc_target = torch.trapz(targets, dim=1).mean() # auc_prediction = torch.trapz(predictions, dim=1).mean() # l1 loss return ( predictions[:, :, 0].sum(1) - auc_threshold ).mean() # + F.l1_loss(predictions[:,:,0].sum(1), targets[:,:,0].sum(1)) * (targets[:,:,0].sum(1) - auc_threshold).mean() def mse_with_auc(predictions, targets, auc_threshold=None, alpha=10.0): # Compute the mean squared error loss mse_loss = F.mse_loss(predictions, targets) # Compute the area under the curve (AUC) using the trapezoidal rule auc = torch.trapz(predictions, dim=1).mean() # Penalize if AUC exceeds the threshold auc_penalty = torch.abs(auc - auc_threshold) # Combine the losses total_loss = mse_loss + alpha * auc_penalty # Adjust the penalty weight as needed return total_loss if __name__ == "__main__": pass