""" Based on https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py """ import math from typing import Any, Dict, Iterable, Optional, Sequence, Union import blobfile as bf import numpy as np import torch as th import yaml def diffusion_from_config(config: Union[str, Dict[str, Any]]) -> "GaussianDiffusion": if isinstance(config, str): with bf.BlobFile(config, "rb") as f: obj = yaml.load(f, Loader=yaml.SafeLoader) return diffusion_from_config(obj) schedule = config["schedule"] steps = config["timesteps"] respace = config.get("respacing", None) mean_type = config.get("mean_type", "epsilon") betas = get_named_beta_schedule(schedule, steps, **config.get("schedule_args", {})) channel_scales = config.get("channel_scales", None) channel_biases = config.get("channel_biases", None) if channel_scales is not None: channel_scales = np.array(channel_scales) if channel_biases is not None: channel_biases = np.array(channel_biases) kwargs = dict( betas=betas, model_mean_type=mean_type, model_var_type="learned_range", loss_type="mse", channel_scales=channel_scales, channel_biases=channel_biases, ) if respace is None: return GaussianDiffusion(**kwargs) else: return SpacedDiffusion(use_timesteps=space_timesteps(steps, respace), **kwargs) def get_beta_schedule(beta_schedule, *, beta_start, beta_end, num_diffusion_timesteps): """ This is the deprecated API for creating beta schedules. See get_named_beta_schedule() for the new library of schedules. """ if beta_schedule == "linear": betas = np.linspace(beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64) else: raise NotImplementedError(beta_schedule) assert betas.shape == (num_diffusion_timesteps,) return betas def get_named_beta_schedule(schedule_name, num_diffusion_timesteps, **extra_args: float): """ 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 return get_beta_schedule( "linear", beta_start=scale * 0.0001, beta_end=scale * 0.02, num_diffusion_timesteps=num_diffusion_timesteps, ) 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, ) elif schedule_name == "inv_parabola": exponent = extra_args.get("power", 2.0) return betas_for_alpha_bar( num_diffusion_timesteps, lambda t: 1 - t**exponent, ) elif schedule_name == "translated_parabola": exponent = extra_args.get("power", 2.0) return betas_for_alpha_bar( num_diffusion_timesteps, lambda t: (1 - t) ** exponent, ) elif schedule_name == "exp": coefficient = extra_args.get("coefficient", -12.0) return betas_for_alpha_bar(num_diffusion_timesteps, lambda t: math.exp(t * coefficient)) 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) def space_timesteps(num_timesteps, section_counts): """ Create a list of timesteps to use from an original diffusion process, given the number of timesteps we want to take from equally-sized portions of the original process. For example, if there's 300 timesteps and the section counts are [10,15,20] then the first 100 timesteps are strided to be 10 timesteps, the second 100 are strided to be 15 timesteps, and the final 100 are strided to be 20. :param num_timesteps: the number of diffusion steps in the original process to divide up. :param section_counts: either a list of numbers, or a string containing comma-separated numbers, indicating the step count per section. As a special case, use "ddimN" where N is a number of steps to use the striding from the DDIM paper. :return: a set of diffusion steps from the original process to use. """ if isinstance(section_counts, str): if section_counts.startswith("ddim"): desired_count = int(section_counts[len("ddim") :]) for i in range(1, num_timesteps): if len(range(0, num_timesteps, i)) == desired_count: return set(range(0, num_timesteps, i)) raise ValueError(f"cannot create exactly {num_timesteps} steps with an integer stride") elif section_counts.startswith("exact"): res = set(int(x) for x in section_counts[len("exact") :].split(",")) for x in res: if x < 0 or x >= num_timesteps: raise ValueError(f"timestep out of bounds: {x}") return res section_counts = [int(x) for x in section_counts.split(",")] size_per = num_timesteps // len(section_counts) extra = num_timesteps % len(section_counts) start_idx = 0 all_steps = [] for i, section_count in enumerate(section_counts): size = size_per + (1 if i < extra else 0) if size < section_count: raise ValueError(f"cannot divide section of {size} steps into {section_count}") if section_count <= 1: frac_stride = 1 else: frac_stride = (size - 1) / (section_count - 1) cur_idx = 0.0 taken_steps = [] for _ in range(section_count): taken_steps.append(start_idx + round(cur_idx)) cur_idx += frac_stride all_steps += taken_steps start_idx += size return set(all_steps) class GaussianDiffusion: """ Utilities for training and sampling diffusion models. Ported directly from here: https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42 :param betas: a 1-D array of betas for each diffusion timestep from T to 1. :param model_mean_type: a string determining what the model outputs. :param model_var_type: a string determining how variance is output. :param loss_type: a string determining the loss function to use. :param discretized_t0: if True, use discrete gaussian loss for t=0. Only makes sense for images. :param channel_scales: a multiplier to apply to x_start in training_losses and sampling functions. """ def __init__( self, *, betas: Sequence[float], model_mean_type: str, model_var_type: str, loss_type: str, discretized_t0: bool = False, channel_scales: Optional[np.ndarray] = None, channel_biases: Optional[np.ndarray] = None, ): self.model_mean_type = model_mean_type self.model_var_type = model_var_type self.loss_type = loss_type self.discretized_t0 = discretized_t0 self.channel_scales = channel_scales self.channel_biases = channel_biases # 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) ) # below: 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 get_sigmas(self, t): return _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, t.shape) 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=False, 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,) model_output = model(x, t, **model_kwargs) if isinstance(model_output, tuple): model_output, extra = model_output else: extra = None if self.model_var_type in ["learned", "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.model_var_type == "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. "fixed_large": ( np.append(self.posterior_variance[1], self.betas[1:]), np.log(np.append(self.posterior_variance[1], self.betas[1:])), ), "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) 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 == "x_prev": 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 ["x_start", "epsilon"]: if self.model_mean_type == "x_start": 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, "extra": extra, } 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 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, t, **(model_kwargs or {})) 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, t, **(model_kwargs or {})) 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=False, 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) nonzero_mask = ( (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) ) # no noise when t == 0 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=False, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, temp=1.0, ): """ 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, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, device=device, progress=progress, temp=temp, ): final = sample return final["sample"] def p_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=False, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, temp=1.0, ): """ 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) * temp 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) for i in indices: t = th.tensor([i] * shape[0], device=device) 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 self.unscale_out_dict(out) img = out["sample"] def ddim_sample( self, model, x, t, clip_denoised=False, 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 ) nonzero_mask = ( (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) ) # no noise when t == 0 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=False, denoised_fn=None, cond_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, ) 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 = ( _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=False, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, eta=0.0, temp=1.0, ): """ 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, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, device=device, progress=progress, eta=eta, temp=temp, ): final = sample return final["sample"] def ddim_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=False, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, eta=0.0, temp=1.0, ): """ 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) * temp 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) for i in indices: t = th.tensor([i] * shape[0], device=device) 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 self.unscale_out_dict(out) img = out["sample"] def _vb_terms_bpd(self, model, x_start, x_t, t, clip_denoised=False, 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 = mean_flat(kl) / np.log(2.0) decoder_nll = -discretized_gaussian_log_likelihood( x_start, means=out["mean"], log_scales=0.5 * out["log_variance"] ) if not self.discretized_t0: decoder_nll = th.zeros_like(decoder_nll) assert decoder_nll.shape == x_start.shape decoder_nll = mean_flat(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)) output = th.where((t == 0), decoder_nll, kl) return { "output": output, "pred_xstart": out["pred_xstart"], "extra": out["extra"], } def training_losses( self, model, x_start, t, model_kwargs=None, noise=None ) -> Dict[str, th.Tensor]: """ 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. """ x_start = self.scale_channels(x_start) if model_kwargs is None: model_kwargs = {} if noise is None: noise = th.randn_like(x_start) x_t = self.q_sample(x_start, t, noise=noise) terms = {} if self.loss_type == "kl" or self.loss_type == "rescaled_kl": vb_terms = self._vb_terms_bpd( model=model, x_start=x_start, x_t=x_t, t=t, clip_denoised=False, model_kwargs=model_kwargs, ) terms["loss"] = vb_terms["output"] if self.loss_type == "rescaled_kl": terms["loss"] *= self.num_timesteps extra = vb_terms["extra"] elif self.loss_type == "mse" or self.loss_type == "rescaled_mse": model_output = model(x_t, t, **model_kwargs) if isinstance(model_output, tuple): model_output, extra = model_output else: extra = {} if self.model_var_type in [ "learned", "learned_range", ]: B, C = x_t.shape[:2] assert model_output.shape == ( B, C * 2, *x_t.shape[2:], ), f"{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"] if self.loss_type == "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 target = { "x_prev": self.q_posterior_mean_variance(x_start=x_start, x_t=x_t, t=t)[0], "x_start": x_start, "epsilon": noise, }[self.model_mean_type] assert model_output.shape == target.shape == x_start.shape terms["mse"] = mean_flat((target - model_output) ** 2) if "vb" in terms: terms["loss"] = terms["mse"] + terms["vb"] else: terms["loss"] = terms["mse"] else: raise NotImplementedError(self.loss_type) if "losses" in extra: terms.update({k: loss for k, (loss, _scale) in extra["losses"].items()}) for loss, scale in extra["losses"].values(): terms["loss"] = terms["loss"] + loss * scale 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=False, 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 = 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 scale_channels(self, x: th.Tensor) -> th.Tensor: if self.channel_scales is not None: x = x * th.from_numpy(self.channel_scales).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) if self.channel_biases is not None: x = x + th.from_numpy(self.channel_biases).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) return x def unscale_channels(self, x: th.Tensor) -> th.Tensor: if self.channel_biases is not None: x = x - th.from_numpy(self.channel_biases).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) if self.channel_scales is not None: x = x / th.from_numpy(self.channel_scales).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) return x def unscale_out_dict( self, out: Dict[str, Union[th.Tensor, Any]] ) -> Dict[str, Union[th.Tensor, Any]]: return { k: (self.unscale_channels(v) if isinstance(v, th.Tensor) else v) for k, v in out.items() } class SpacedDiffusion(GaussianDiffusion): """ A diffusion process which can skip steps in a base diffusion process. :param use_timesteps: (unordered) timesteps from the original diffusion process to retain. :param kwargs: the kwargs to create the base diffusion process. """ def __init__(self, use_timesteps: Iterable[int], **kwargs): self.use_timesteps = set(use_timesteps) self.timestep_map = [] self.original_num_steps = len(kwargs["betas"]) base_diffusion = GaussianDiffusion(**kwargs) # pylint: disable=missing-kwoa last_alpha_cumprod = 1.0 new_betas = [] for i, alpha_cumprod in enumerate(base_diffusion.alphas_cumprod): if i in self.use_timesteps: new_betas.append(1 - alpha_cumprod / last_alpha_cumprod) last_alpha_cumprod = alpha_cumprod self.timestep_map.append(i) kwargs["betas"] = np.array(new_betas) super().__init__(**kwargs) def p_mean_variance(self, model, *args, **kwargs): return super().p_mean_variance(self._wrap_model(model), *args, **kwargs) def training_losses(self, model, *args, **kwargs): return super().training_losses(self._wrap_model(model), *args, **kwargs) def condition_mean(self, cond_fn, *args, **kwargs): return super().condition_mean(self._wrap_model(cond_fn), *args, **kwargs) def condition_score(self, cond_fn, *args, **kwargs): return super().condition_score(self._wrap_model(cond_fn), *args, **kwargs) def _wrap_model(self, model): if isinstance(model, _WrappedModel): return model return _WrappedModel(model, self.timestep_map, self.original_num_steps) class _WrappedModel: def __init__(self, model, timestep_map, original_num_steps): self.model = model self.timestep_map = timestep_map self.original_num_steps = original_num_steps def __call__(self, x, ts, **kwargs): map_tensor = th.tensor(self.timestep_map, device=ts.device, dtype=ts.dtype) new_ts = map_tensor[ts] return self.model(x, new_ts, **kwargs) 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 + th.zeros(broadcast_shape, device=timesteps.device) def normal_kl(mean1, logvar1, mean2, logvar2): """ Compute the KL divergence between two gaussians. Shapes are automatically broadcasted, so batches can be compared to scalars, among other use cases. """ tensor = None for obj in (mean1, logvar1, mean2, logvar2): if isinstance(obj, th.Tensor): tensor = obj break assert tensor is not None, "at least one argument must be a Tensor" # Force variances to be Tensors. Broadcasting helps convert scalars to # Tensors, but it does not work for th.exp(). logvar1, logvar2 = [ x if isinstance(x, th.Tensor) else th.tensor(x).to(tensor) for x in (logvar1, logvar2) ] return 0.5 * ( -1.0 + logvar2 - logvar1 + th.exp(logvar1 - logvar2) + ((mean1 - mean2) ** 2) * th.exp(-logvar2) ) def approx_standard_normal_cdf(x): """ A fast approximation of the cumulative distribution function of the standard normal. """ return 0.5 * (1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3)))) def discretized_gaussian_log_likelihood(x, *, means, log_scales): """ Compute the log-likelihood of a Gaussian distribution discretizing to a given image. :param x: the target images. It is assumed that this was uint8 values, rescaled to the range [-1, 1]. :param means: the Gaussian mean Tensor. :param log_scales: the Gaussian log stddev Tensor. :return: a tensor like x of log probabilities (in nats). """ assert x.shape == means.shape == log_scales.shape centered_x = x - means inv_stdv = th.exp(-log_scales) plus_in = inv_stdv * (centered_x + 1.0 / 255.0) cdf_plus = approx_standard_normal_cdf(plus_in) min_in = inv_stdv * (centered_x - 1.0 / 255.0) cdf_min = approx_standard_normal_cdf(min_in) log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12)) log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12)) cdf_delta = cdf_plus - cdf_min log_probs = th.where( x < -0.999, log_cdf_plus, th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))), ) assert log_probs.shape == x.shape return log_probs def mean_flat(tensor): """ Take the mean over all non-batch dimensions. """ return tensor.flatten(1).mean(1)