""" This code started out as a PyTorch port of Ho et al's diffusion models: https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py Docstrings have been added, as well as DDIM sampling and a new collection of beta schedules. """ import enum import math import random import numpy as np import torch import torch as th from tqdm import tqdm from models.diffusion.nn import mean_flat from models.diffusion.losses import normal_kl, discretized_gaussian_log_likelihood def causal_timestep_adjustment(t, S, num_timesteps, causal_slope=1, add_jitter=True): """ Remaps [t] from a batch of integers into a causal sequence [S] long where each sequence element is [causal_slope] timesteps advanced from the previous sequence element. At t=0, the sequence is all 0s and at t=[num_timesteps], the sequence is all [num_timesteps]. As a result of the last property, longer sequences will have larger "gaps" between them in continuous space. This must be considered at inference time. :param t: Batched timestep integers :param S: Sequence length. :param num_timesteps: Number of total timesteps. :param causal_slope: The causal slope. Ex: "2" means each sequence element will be 2 timesteps ahead of its predecessor. :param add_jitter: Whether or not to add random jitter into the extra gaps between timesteps added by this function. Should be true for training and false for inference. :return: [b,S] sequence of timestep integers. """ S_sloped = causal_slope * (S-1) # This algorithm for adding causality does so by simply adding S_sloped additional timesteps. To make this # actually work, we map the existing t from the timescale specified to the model to the causal timescale: adj_t = t * (num_timesteps + S_sloped) // num_timesteps adj_t = adj_t - S_sloped if add_jitter: t_gap = (num_timesteps + S_sloped) / num_timesteps jitter = (2*random.random()-1) * t_gap adj_t = (adj_t+jitter).clamp(-S_sloped, num_timesteps) # Now use the re-mapped adj_t to create a timestep vector that propagates across the sequence with the specified slope. t = adj_t.unsqueeze(1).repeat(1, S) t = (t + torch.arange(0, S, device=t.device) * causal_slope).clamp(0, num_timesteps).long() return t def get_named_beta_schedule(schedule_name, num_diffusion_timesteps): """ Get a pre-defined beta schedule for the given name. The beta schedule library consists of beta schedules which remain similar in the limit of num_diffusion_timesteps. Beta schedules may be added, but should not be removed or changed once they are committed to maintain backwards compatibility. """ if schedule_name == "linear": # Linear schedule from Ho et al, extended to work for any number of # diffusion steps. scale = 1000 / num_diffusion_timesteps beta_start = scale * 0.0001 beta_end = scale * 0.02 return np.linspace( beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64 ) elif schedule_name == "cosine": return betas_for_alpha_bar( num_diffusion_timesteps, lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2, ) else: raise NotImplementedError(f"unknown beta schedule: {schedule_name}") def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999): """ Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of (1-beta) over time from t = [0,1]. :param num_diffusion_timesteps: the number of betas to produce. :param alpha_bar: a lambda that takes an argument t from 0 to 1 and produces the cumulative product of (1-beta) up to that part of the diffusion process. :param max_beta: the maximum beta to use; use values lower than 1 to prevent singularities. """ betas = [] for i in range(num_diffusion_timesteps): t1 = i / num_diffusion_timesteps t2 = (i + 1) / num_diffusion_timesteps betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta)) return np.array(betas) class ModelMeanType(enum.Enum): """ Which type of output the model predicts. """ PREVIOUS_X = 'previous_x' # the model predicts x_{t-1} START_X = 'start_x' # the model predicts x_0 EPSILON = 'epsilon' # the model predicts epsilon class ModelVarType(enum.Enum): """ What is used as the model's output variance. The LEARNED_RANGE option has been added to allow the model to predict values between FIXED_SMALL and FIXED_LARGE, making its job easier. """ LEARNED = 'learned' FIXED_SMALL = 'fixed_small' FIXED_LARGE = 'fixed_large' LEARNED_RANGE = 'learned_range' class LossType(enum.Enum): MSE = 'mse' # use raw MSE loss (and KL when learning variances) RESCALED_MSE = 'rescaled_mse' # use raw MSE loss (with RESCALED_KL when learning variances) KL = 'kl' # use the variational lower-bound RESCALED_KL = 'rescaled_kl' # like KL, but rescale to estimate the full VLB def is_vb(self): return self == LossType.KL or self == LossType.RESCALED_KL class GaussianDiffusion: """ Utilities for training and sampling diffusion models. Ported directly from here, and then adapted over time to further experimentation. https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42 :param betas: a 1-D numpy array of betas for each diffusion timestep, starting at T and going to 1. :param model_mean_type: a ModelMeanType determining what the model outputs. :param model_var_type: a ModelVarType determining how variance is output. :param loss_type: a LossType determining the loss function to use. :param rescale_timesteps: if True, pass floating point timesteps into the model so that they are always scaled like in the original paper (0 to 1000). """ def __init__( self, *, betas, model_mean_type, model_var_type, loss_type, rescale_timesteps=False, conditioning_free=False, conditioning_free_k=1, ramp_conditioning_free=True, ): self.model_mean_type = ModelMeanType(model_mean_type) self.model_var_type = ModelVarType(model_var_type) self.loss_type = LossType(loss_type) self.rescale_timesteps = rescale_timesteps self.conditioning_free = conditioning_free self.conditioning_free_k = conditioning_free_k self.ramp_conditioning_free = ramp_conditioning_free # Use float64 for accuracy. betas = np.array(betas, dtype=np.float64) self.betas = betas assert len(betas.shape) == 1, "betas must be 1-D" assert (betas > 0).all() and (betas <= 1).all() self.num_timesteps = int(betas.shape[0]) alphas = 1.0 - betas self.alphas_cumprod = np.cumprod(alphas, axis=0) self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1]) self.alphas_cumprod_next = np.append(self.alphas_cumprod[1:], 0.0) assert self.alphas_cumprod_prev.shape == (self.num_timesteps,) # calculations for diffusion q(x_t | x_{t-1}) and others self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod) self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod) self.log_one_minus_alphas_cumprod = np.log(1.0 - self.alphas_cumprod) self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod) self.sqrt_recipm1_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod - 1) # calculations for posterior q(x_{t-1} | x_t, x_0) self.posterior_variance = ( betas * (1.0 - self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod) ) # log calculation clipped because the posterior variance is 0 at the # beginning of the diffusion chain. self.posterior_log_variance_clipped = np.log( np.append(self.posterior_variance[1], self.posterior_variance[1:]) ) self.posterior_mean_coef1 = ( betas * np.sqrt(self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod) ) self.posterior_mean_coef2 = ( (1.0 - self.alphas_cumprod_prev) * np.sqrt(alphas) / (1.0 - self.alphas_cumprod) ) def q_mean_variance(self, x_start, t): """ Get the distribution q(x_t | x_0). :param x_start: the [N x C x ...] tensor of noiseless inputs. :param t: the number of diffusion steps (minus 1). Here, 0 means one step. :return: A tuple (mean, variance, log_variance), all of x_start's shape. """ mean = ( _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start ) variance = _extract_into_tensor(1.0 - self.alphas_cumprod, t, x_start.shape) log_variance = _extract_into_tensor( self.log_one_minus_alphas_cumprod, t, x_start.shape ) return mean, variance, log_variance def q_sample(self, x_start, t, noise=None): """ Diffuse the data for a given number of diffusion steps. In other words, sample from q(x_t | x_0). :param x_start: the initial data batch. :param t: the number of diffusion steps (minus 1). Here, 0 means one step. :param noise: if specified, the split-out normal noise. :return: A noisy version of x_start. """ if noise is None: noise = th.randn_like(x_start) assert noise.shape == x_start.shape return ( _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start + _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise ) def q_posterior_mean_variance(self, x_start, x_t, t): """ Compute the mean and variance of the diffusion posterior: q(x_{t-1} | x_t, x_0) """ assert x_start.shape == x_t.shape posterior_mean = ( _extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) * x_start + _extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) * x_t ) posterior_variance = _extract_into_tensor(self.posterior_variance, t, x_t.shape) posterior_log_variance_clipped = _extract_into_tensor( self.posterior_log_variance_clipped, t, x_t.shape ) assert ( posterior_mean.shape[0] == posterior_variance.shape[0] == posterior_log_variance_clipped.shape[0] == x_start.shape[0] ) return posterior_mean, posterior_variance, posterior_log_variance_clipped def p_mean_variance( self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None ): """ Apply the model to get p(x_{t-1} | x_t), as well as a prediction of the initial x, x_0. :param model: the model, which takes a signal and a batch of timesteps as input. :param x: the [N x C x ...] tensor at time t. :param t: a 1-D Tensor of timesteps. :param clip_denoised: if True, clip the denoised signal into [-1, 1]. :param denoised_fn: if not None, a function which applies to the x_start prediction before it is used to sample. Applies before clip_denoised. :param model_kwargs: if not None, a dict of extra keyword arguments to pass to the model. This can be used for conditioning. :return: a dict with the following keys: - 'mean': the model mean output. - 'variance': the model variance output. - 'log_variance': the log of 'variance'. - 'pred_xstart': the prediction for x_0. """ if model_kwargs is None: model_kwargs = {} B, C = x.shape[:2] assert t.shape == (B,) or t.shape == (B,1,x.shape[-1]) model_output = model(x, self._scale_timesteps(t), **model_kwargs) if self.conditioning_free: model_output_no_conditioning = model(x, self._scale_timesteps(t), conditioning_free=True, **model_kwargs) if self.model_var_type in [ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE]: assert model_output.shape == (B, C * 2, *x.shape[2:]) model_output, model_var_values = th.split(model_output, C, dim=1) if self.conditioning_free: model_output_no_conditioning, _ = th.split(model_output_no_conditioning, C, dim=1) if self.model_var_type == ModelVarType.LEARNED: model_log_variance = model_var_values model_variance = th.exp(model_log_variance) else: min_log = _extract_into_tensor( self.posterior_log_variance_clipped, t, x.shape ) max_log = _extract_into_tensor(np.log(self.betas), t, x.shape) # The model_var_values is [-1, 1] for [min_var, max_var]. frac = (model_var_values + 1) / 2 model_log_variance = frac * max_log + (1 - frac) * min_log model_variance = th.exp(model_log_variance) else: model_variance, model_log_variance = { # for fixedlarge, we set the initial (log-)variance like so # to get a better decoder log likelihood. ModelVarType.FIXED_LARGE: ( np.append(self.posterior_variance[1], self.betas[1:]), np.log(np.append(self.posterior_variance[1], self.betas[1:])), ), ModelVarType.FIXED_SMALL: ( self.posterior_variance, self.posterior_log_variance_clipped, ), }[self.model_var_type] model_variance = _extract_into_tensor(model_variance, t, x.shape) model_log_variance = _extract_into_tensor(model_log_variance, t, x.shape) if self.conditioning_free: if self.ramp_conditioning_free: assert t.shape[0] == 1 # This should only be used in inference. cfk = self.conditioning_free_k * (1 - self._scale_timesteps(t).float().mean().item() / self.num_timesteps) else: cfk = self.conditioning_free_k model_output = (1 + cfk) * model_output - cfk * model_output_no_conditioning def process_xstart(x): if denoised_fn is not None: x = denoised_fn(x) if clip_denoised: return x.clamp(-1, 1) return x if self.model_mean_type == ModelMeanType.PREVIOUS_X: pred_xstart = process_xstart( self._predict_xstart_from_xprev(x_t=x, t=t, xprev=model_output) ) model_mean = model_output elif self.model_mean_type in [ModelMeanType.START_X, ModelMeanType.EPSILON]: if self.model_mean_type == ModelMeanType.START_X: pred_xstart = process_xstart(model_output) else: pred_xstart = process_xstart( self._predict_xstart_from_eps(x_t=x, t=t, eps=model_output) ) model_mean, _, _ = self.q_posterior_mean_variance( x_start=pred_xstart, x_t=x, t=t ) else: raise NotImplementedError(self.model_mean_type) assert ( model_mean.shape == model_log_variance.shape == pred_xstart.shape == x.shape ) return { "mean": model_mean, "variance": model_variance, "log_variance": model_log_variance, "pred_xstart": pred_xstart, } def _predict_xstart_from_eps(self, x_t, t, eps): assert x_t.shape == eps.shape return ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * eps ) def _predict_xstart_from_xprev(self, x_t, t, xprev): assert x_t.shape == xprev.shape return ( # (xprev - coef2*x_t) / coef1 _extract_into_tensor(1.0 / self.posterior_mean_coef1, t, x_t.shape) * xprev - _extract_into_tensor( self.posterior_mean_coef2 / self.posterior_mean_coef1, t, x_t.shape ) * x_t ) def _predict_eps_from_xstart(self, x_t, t, pred_xstart): return ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - pred_xstart ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) def _scale_timesteps(self, t): if self.rescale_timesteps: return t.float() * (1000.0 / self.num_timesteps) return t def condition_mean(self, cond_fn, p_mean_var, x, t, model_kwargs=None): """ Compute the mean for the previous step, given a function cond_fn that computes the gradient of a conditional log probability with respect to x. In particular, cond_fn computes grad(log(p(y|x))), and we want to condition on y. This uses the conditioning strategy from Sohl-Dickstein et al. (2015). """ gradient = cond_fn(x, self._scale_timesteps(t), **model_kwargs) new_mean = ( p_mean_var["mean"].float() + p_mean_var["variance"] * gradient.float() ) return new_mean def condition_score(self, cond_fn, p_mean_var, x, t, model_kwargs=None): """ Compute what the p_mean_variance output would have been, should the model's score function be conditioned by cond_fn. See condition_mean() for details on cond_fn. Unlike condition_mean(), this instead uses the conditioning strategy from Song et al (2020). """ alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape) eps = self._predict_eps_from_xstart(x, t, p_mean_var["pred_xstart"]) eps = eps - (1 - alpha_bar).sqrt() * cond_fn( x, self._scale_timesteps(t), **model_kwargs ) out = p_mean_var.copy() out["pred_xstart"] = self._predict_xstart_from_eps(x, t, eps) out["mean"], _, _ = self.q_posterior_mean_variance( x_start=out["pred_xstart"], x_t=x, t=t ) return out def p_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, ): """ Sample x_{t-1} from the model at the given timestep. :param model: the model to sample from. :param x: the current tensor at x_{t-1}. :param t: the value of t, starting at 0 for the first diffusion step. :param clip_denoised: if True, clip the x_start prediction to [-1, 1]. :param denoised_fn: if not None, a function which applies to the x_start prediction before it is used to sample. :param cond_fn: if not None, this is a gradient function that acts similarly to the model. :param model_kwargs: if not None, a dict of extra keyword arguments to pass to the model. This can be used for conditioning. :return: a dict containing the following keys: - 'sample': a random sample from the model. - 'pred_xstart': a prediction of x_0. """ out = self.p_mean_variance( model, x, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, model_kwargs=model_kwargs, ) noise = th.randn_like(x) if len(t.shape) == 1: nonzero_mask = ( (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) ) # no noise when t == 0 else: nonzero_mask = (t != 0).float() if cond_fn is not None: out["mean"] = self.condition_mean( cond_fn, out, x, t, model_kwargs=model_kwargs ) sample = out["mean"] + nonzero_mask * th.exp(0.5 * out["log_variance"]) * noise return {"sample": sample, "pred_xstart": out["pred_xstart"]} def p_sample_loop( self, model, shape, noise=None, clip_denoised=True, causal=False, causal_slope=1, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, ): """ Generate samples from the model. :param model: the model module. :param shape: the shape of the samples, (N, C, H, W). :param noise: if specified, the noise from the encoder to sample. Should be of the same shape as `shape`. :param clip_denoised: if True, clip x_start predictions to [-1, 1]. :param denoised_fn: if not None, a function which applies to the x_start prediction before it is used to sample. :param cond_fn: if not None, this is a gradient function that acts similarly to the model. :param model_kwargs: if not None, a dict of extra keyword arguments to pass to the model. This can be used for conditioning. :param device: if specified, the device to create the samples on. If not specified, use a model parameter's device. :param progress: if True, show a tqdm progress bar. :return: a non-differentiable batch of samples. """ final = None for sample in self.p_sample_loop_progressive( model, shape, noise=noise, clip_denoised=clip_denoised, causal=causal, causal_slope=causal_slope, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, device=device, progress=progress, ): final = sample return final["sample"] def p_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, causal=False, causal_slope=1, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, ): """ Generate samples from the model and yield intermediate samples from each timestep of diffusion. Arguments are the same as p_sample_loop(). Returns a generator over dicts, where each dict is the return value of p_sample(). """ if device is None: device = next(model.parameters()).device assert isinstance(shape, (tuple, list)) if noise is not None: img = noise else: img = th.randn(*shape, device=device) indices = list(range(self.num_timesteps))[::-1] orig_img = img for i in tqdm(indices): t = th.tensor([i] * shape[0], device=device) mask = torch.zeros_like(img) if causal: t = causal_timestep_adjustment(t, shape[-1], self.num_timesteps, causal_slope, add_jitter=False).unsqueeze(1) mask = t == self.num_timesteps t[mask] = self.num_timesteps-1 mask = mask.repeat(img.shape[0], img.shape[1], 1) with th.no_grad(): out = self.p_sample( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, ) yield out img = out["sample"] if torch.any(mask): img[mask] = orig_img[mask] # For causal diffusion, keep resetting these predictions until they are unmasked. def p_sample_loop_with_guidance( self, model, guidance_input, mask, noise=None, clip_denoised=True, causal=False, causal_slope=1, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, ): if device is None: device = next(model.parameters()).device shape = guidance_input.shape if noise is None: noise = th.randn(*shape, device=device) indices = list(range(self.num_timesteps))[::-1] img = noise for i in tqdm(indices): t = th.tensor([i] * shape[0], device=device) with th.no_grad(): out = self.p_sample( model, img, t, clip_denoised=clip_denoised, causal=causal, causal_slope=causal_slope, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, ) model_driven_out = out["sample"] * mask.logical_not() guidance_driven_out = self.q_sample(guidance_input, t, noise=noise) * mask img = model_driven_out + guidance_driven_out return img def ddim_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, eta=0.0, ): """ Sample x_{t-1} from the model using DDIM. Same usage as p_sample(). """ out = self.p_mean_variance( model, x, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, model_kwargs=model_kwargs, ) if cond_fn is not None: out = self.condition_score(cond_fn, out, x, t, model_kwargs=model_kwargs) # Usually our model outputs epsilon, but we re-derive it # in case we used x_start or x_prev prediction. eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"]) alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape) alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t, x.shape) sigma = ( eta * th.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar)) * th.sqrt(1 - alpha_bar / alpha_bar_prev) ) # Equation 12. noise = th.randn_like(x) mean_pred = ( out["pred_xstart"] * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev - sigma ** 2) * eps ) if len(t.shape) == 2: nonzero_mask = ( (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) ) # no noise when t == 0 else: nonzero_mask = (t != 0).float() sample = mean_pred + nonzero_mask * sigma * noise return {"sample": sample, "pred_xstart": out["pred_xstart"]} def ddim_reverse_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None, eta=0.0, ): """ Sample x_{t+1} from the model using DDIM reverse ODE. """ assert eta == 0.0, "Reverse ODE only for deterministic path" out = self.p_mean_variance( model, x, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, model_kwargs=model_kwargs, ) # Usually our model outputs epsilon, but we re-derive it # in case we used x_start or x_prev prediction. eps = ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x.shape) * x - out["pred_xstart"] ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x.shape) alpha_bar_next = _extract_into_tensor(self.alphas_cumprod_next, t, x.shape) # Equation 12. reversed mean_pred = ( out["pred_xstart"] * th.sqrt(alpha_bar_next) + th.sqrt(1 - alpha_bar_next) * eps ) return {"sample": mean_pred, "pred_xstart": out["pred_xstart"]} def ddim_sample_loop( self, model, shape, noise=None, clip_denoised=True, causal=False, causal_slope=1, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=True, eta=0.0, ): """ Generate samples from the model using DDIM. Same usage as p_sample_loop(). """ final = None for sample in self.ddim_sample_loop_progressive( model, shape, noise=noise, clip_denoised=clip_denoised, causal=causal, causal_slope=causal_slope, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, device=device, progress=progress, eta=eta, ): final = sample return final["sample"] def ddim_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, causal=False, causal_slope=1, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=True, eta=0.0, ): """ Use DDIM to sample from the model and yield intermediate samples from each timestep of DDIM. Same usage as p_sample_loop_progressive(). """ if device is None: device = next(model.parameters()).device assert isinstance(shape, (tuple, list)) if noise is not None: img = noise else: img = th.randn(*shape, device=device) indices = list(range(self.num_timesteps))[::-1] if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices) orig_img = img for i in indices: t = th.tensor([i] * shape[0], device=device) mask = torch.zeros_like(img) if causal: t = causal_timestep_adjustment(t, shape[-1], self.num_timesteps, causal_slope, add_jitter=False).unsqueeze(1) mask = t == self.num_timesteps t[mask] = self.num_timesteps-1 mask = mask.repeat(img.shape[0], img.shape[1], 1) with th.no_grad(): out = self.ddim_sample( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, eta=eta, ) yield out img = out["sample"] if torch.any(mask): img[mask] = orig_img[mask] # For causal diffusion, keep resetting these predictions until they are unmasked. def _vb_terms_bpd( self, model, x_start, x_t, t, clip_denoised=True, model_kwargs=None ): """ Get a term for the variational lower-bound. The resulting units are bits (rather than nats, as one might expect). This allows for comparison to other papers. :return: a dict with the following keys: - 'output': a shape [N] tensor of NLLs or KLs. - 'pred_xstart': the x_0 predictions. """ true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance( x_start=x_start, x_t=x_t, t=t ) out = self.p_mean_variance( model, x_t, t, clip_denoised=clip_denoised, model_kwargs=model_kwargs ) kl = normal_kl( true_mean, true_log_variance_clipped, out["mean"], out["log_variance"] ) kl = kl / np.log(2.0) decoder_nll = -discretized_gaussian_log_likelihood( x_start, means=out["mean"], log_scales=0.5 * out["log_variance"] ) assert decoder_nll.shape == x_start.shape decoder_nll = decoder_nll / np.log(2.0) # At the first timestep return the decoder NLL, # otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t)) if len(t.shape) == 1: output = th.where((t == 0).view(-1, 1, 1), decoder_nll, kl) else: output = th.where((t == 0), decoder_nll, kl) return {"output": output, "pred_xstart": out["pred_xstart"]} def causal_training_losses(self, model, x_start, t, causal_slope=1, model_kwargs=None, noise=None, channel_balancing_fn=None): """ Compute training losses for a causal diffusion process. """ assert len(x_start.shape) == 3, "causal_training_losses assumes a 1d sequence with the axis being the time axis." ct = causal_timestep_adjustment(t, x_start.shape[-1], self.num_timesteps, causal_slope, add_jitter=True) ct = ct.unsqueeze(1) # Necessary to make the output shape compatible with x_start. return self.training_losses(model, x_start, ct, model_kwargs, noise, channel_balancing_fn) def training_losses(self, model, x_start, t, model_kwargs=None, noise=None, channel_balancing_fn=None): """ Compute training losses for a single timestep. :param model: the model to evaluate loss on. :param x_start: the [N x C x ...] tensor of inputs. :param t: a batch of timestep indices. :param model_kwargs: if not None, a dict of extra keyword arguments to pass to the model. This can be used for conditioning. :param noise: if specified, the specific Gaussian noise to try to remove. :return: a dict with the key "loss" containing a tensor of shape [N]. Some mean or variance settings may also have other keys. """ if model_kwargs is None: model_kwargs = {} if noise is None: noise = th.randn_like(x_start) if len(t.shape) == 3: t_mask = t != self.num_timesteps t[t_mask.logical_not()] = self.num_timesteps-1 else: t_mask = torch.ones_like(x_start) x_t = self.q_sample(x_start, t, noise=noise) terms = {} if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL: # TODO: support multiple model outputs for this mode. terms["loss"] = mean_flat(self._vb_terms_bpd( model=model, x_start=x_start, x_t=x_t, t=t, clip_denoised=False, model_kwargs=model_kwargs, )["output"]) if self.loss_type == LossType.RESCALED_KL: terms["loss"] *= self.num_timesteps elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE: model_outputs = model(x_t, self._scale_timesteps(t), **model_kwargs) if isinstance(model_outputs, tuple): model_output = model_outputs[0] terms['extra_outputs'] = model_outputs[1:] else: model_output = model_outputs if self.model_var_type in [ ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE, ]: B, C = x_t.shape[:2] assert model_output.shape == (B, C * 2, *x_t.shape[2:]) model_output, model_var_values = th.split(model_output, C, dim=1) # Learn the variance using the variational bound, but don't let # it affect our mean prediction. frozen_out = th.cat([model_output.detach(), model_var_values], dim=1) terms["vb"] = self._vb_terms_bpd( model=lambda *args, r=frozen_out: r, x_start=x_start, x_t=x_t, t=t, clip_denoised=False, )["output"] * t_mask if self.loss_type == LossType.RESCALED_MSE: # Divide by 1000 for equivalence with initial implementation. # Without a factor of 1/1000, the VB term hurts the MSE term. terms["vb"] *= self.num_timesteps / 1000.0 if self.model_mean_type == ModelMeanType.PREVIOUS_X: target = self.q_posterior_mean_variance( x_start=x_start, x_t=x_t, t=t )[0] x_start_pred = torch.zeros(x_start) # Not supported. elif self.model_mean_type == ModelMeanType.START_X: target = x_start x_start_pred = model_output elif self.model_mean_type == ModelMeanType.EPSILON: target = noise x_start_pred = self._predict_xstart_from_eps(x_t, t, model_output) else: raise NotImplementedError(self.model_mean_type) assert model_output.shape == target.shape == x_start.shape s_err = t_mask * (target - model_output) ** 2 if channel_balancing_fn is not None: s_err = channel_balancing_fn(s_err) terms["mse_by_batch"] = s_err.reshape(s_err.shape[0], -1).mean(dim=1) terms["mse"] = mean_flat(s_err) terms["x_start_predicted"] = x_start_pred if "vb" in terms: if channel_balancing_fn is not None: terms["vb"] = channel_balancing_fn(terms["vb"]) terms["loss"] = terms["mse"] + mean_flat(terms["vb"]) else: terms["loss"] = terms["mse"] else: raise NotImplementedError(self.loss_type) return terms def _prior_bpd(self, x_start): """ Get the prior KL term for the variational lower-bound, measured in bits-per-dim. This term can't be optimized, as it only depends on the encoder. :param x_start: the [N x C x ...] tensor of inputs. :return: a batch of [N] KL values (in bits), one per batch element. """ batch_size = x_start.shape[0] t = th.tensor([self.num_timesteps - 1] * batch_size, device=x_start.device) qt_mean, _, qt_log_variance = self.q_mean_variance(x_start, t) kl_prior = normal_kl( mean1=qt_mean, logvar1=qt_log_variance, mean2=0.0, logvar2=0.0 ) return mean_flat(kl_prior) / np.log(2.0) def calc_bpd_loop(self, model, x_start, clip_denoised=True, model_kwargs=None): """ Compute the entire variational lower-bound, measured in bits-per-dim, as well as other related quantities. :param model: the model to evaluate loss on. :param x_start: the [N x C x ...] tensor of inputs. :param clip_denoised: if True, clip denoised samples. :param model_kwargs: if not None, a dict of extra keyword arguments to pass to the model. This can be used for conditioning. :return: a dict containing the following keys: - total_bpd: the total variational lower-bound, per batch element. - prior_bpd: the prior term in the lower-bound. - vb: an [N x T] tensor of terms in the lower-bound. - xstart_mse: an [N x T] tensor of x_0 MSEs for each timestep. - mse: an [N x T] tensor of epsilon MSEs for each timestep. """ device = x_start.device batch_size = x_start.shape[0] vb = [] xstart_mse = [] mse = [] for t in list(range(self.num_timesteps))[::-1]: t_batch = th.tensor([t] * batch_size, device=device) noise = th.randn_like(x_start) x_t = self.q_sample(x_start=x_start, t=t_batch, noise=noise) # Calculate VLB term at the current timestep with th.no_grad(): out = mean_flat(self._vb_terms_bpd( model, x_start=x_start, x_t=x_t, t=t_batch, clip_denoised=clip_denoised, model_kwargs=model_kwargs, )) vb.append(out["output"]) xstart_mse.append(mean_flat((out["pred_xstart"] - x_start) ** 2)) eps = self._predict_eps_from_xstart(x_t, t_batch, out["pred_xstart"]) mse.append(mean_flat((eps - noise) ** 2)) vb = th.stack(vb, dim=1) xstart_mse = th.stack(xstart_mse, dim=1) mse = th.stack(mse, dim=1) prior_bpd = self._prior_bpd(x_start) total_bpd = vb.sum(dim=1) + prior_bpd return { "total_bpd": total_bpd, "prior_bpd": prior_bpd, "vb": vb, "xstart_mse": xstart_mse, "mse": mse, } def _extract_into_tensor(arr, timesteps, broadcast_shape): """ Extract values from a 1-D numpy array for a batch of indices. :param arr: the 1-D numpy array. :param timesteps: a tensor of indices into the array to extract. :param broadcast_shape: a larger shape of K dimensions with the batch dimension equal to the length of timesteps. :return: a tensor of shape [batch_size, 1, ...] where the shape has K dims. """ res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float() while len(res.shape) < len(broadcast_shape): res = res[..., None] return res.expand(broadcast_shape) def test_causal_training_losses(): from models.diffusion.respace import SpacedDiffusion from models.diffusion.respace import space_timesteps diff = SpacedDiffusion(use_timesteps=space_timesteps(4000, [4000]), model_mean_type='epsilon', model_var_type='learned_range', loss_type='mse', betas=get_named_beta_schedule('linear', 4000), conditioning_free=False, conditioning_free_k=1) class IdentityTwoArg(torch.nn.Module): def __init__(self): super().__init__() def forward(self, x, *args, **kwargs): return x.repeat(1,2,1) model = IdentityTwoArg() diff.causal_training_losses(model, torch.randn(4,256,400), torch.tensor([500,1000,3000,3500]), causal_slope=4) def graph_causal_timestep_adjustment(): import matplotlib.pyplot as plt S = 400 #slope=4 num_timesteps=4000 for slpe in range(10, 400, 10): slope = slpe / 10 t_res = [] for t in range(num_timesteps, -1, -num_timesteps//50): T = causal_timestep_adjustment(torch.tensor([t]), S, num_timesteps, causal_slope=slope, add_jitter=False)[0] t_res.append(T) plt.plot(T.numpy()) for i in range(len(t_res)): for j in range(len(t_res)): if i == j: continue #assert not torch.all(t_res[i] == t_res[j]) plt.ylim(0,num_timesteps) plt.xlim(0,4000) plt.ylabel('timestep') plt.savefig(f'{slpe}.png') plt.clf() if __name__ == '__main__': #test_causal_training_losses() graph_causal_timestep_adjustment()