""" Copyright (c) Meta Platforms, Inc. and affiliates. All rights reserved. This source code is licensed under the license found in the LICENSE file in the root directory of this source tree. """ """ original code from https://github.com/GuyTevet/motion-diffusion-model/blob/main/diffusion/gaussian_diffusion.py under an MIT license https://github.com/GuyTevet/motion-diffusion-model/blob/main/LICENSE """ import enum import math from copy import deepcopy import numpy as np import torch import torch as th from diffusion.losses import discretized_gaussian_log_likelihood, normal_kl from diffusion.nn import mean_flat, sum_flat def get_named_beta_schedule(schedule_name, num_diffusion_timesteps, scale_betas=1.0): """ 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 = scale_betas * 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 = enum.auto() # the model predicts x_{t-1} START_X = enum.auto() # the model predicts x_0 EPSILON = enum.auto() # 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 = enum.auto() FIXED_SMALL = enum.auto() FIXED_LARGE = enum.auto() LEARNED_RANGE = enum.auto() class LossType(enum.Enum): MSE = enum.auto() # use raw MSE loss (and KL when learning variances) RESCALED_MSE = ( enum.auto() ) # use raw MSE loss (with RESCALED_KL when learning variances) KL = enum.auto() # use the variational lower-bound RESCALED_KL = enum.auto() # 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, lambda_vel=0.0, data_format="pose", model_path=None, ): self.model_mean_type = model_mean_type self.model_var_type = model_var_type self.loss_type = loss_type self.rescale_timesteps = rescale_timesteps self.data_format = data_format self.lambda_vel = lambda_vel if self.lambda_vel > 0.0: assert ( self.loss_type == LossType.MSE ), "Geometric losses are supported by MSE loss type only!" # 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) ) self.l2_loss = lambda a, b: (a - b) ** 2 def masked_l2(self, a, b, mask): loss = self.l2_loss(a, b) loss = sum_flat(loss * mask.float()) n_entries = a.shape[1] * a.shape[2] non_zero_elements = sum_flat(mask) * n_entries mse_loss_val = loss / non_zero_elements return mse_loss_val 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 dataset for a given number of diffusion steps. In other words, sample from q(x_t | x_0). :param x_start: the initial dataset 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, f"x_start: {x_start.shape}, x_t: {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,) model_output = model(x, self._scale_timesteps(t), **model_kwargs) 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) def process_xstart(x): if denoised_fn is not None: x = denoised_fn(x) if clip_denoised: return x.clamp(-1, 1) return x pred_xstart = process_xstart(model_output) pred_xstart = pred_xstart.permute(0, 2, 1).unsqueeze(2) model_mean, _, _ = self.q_posterior_mean_variance( x_start=pred_xstart, x_t=x, t=t ) assert ( model_mean.shape == model_log_variance.shape == pred_xstart.shape == x.shape ), print( f"{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 ( _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_mean_with_grad(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, p_mean_var, **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 condition_score_with_grad(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, p_mean_var, **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, const_noise=False, ): """ 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, ) nonzero_mask = (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) 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_with_grad( 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. """ with th.enable_grad(): x = x.detach().requires_grad_() 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))) if cond_fn is not None: out["mean"] = self.condition_mean_with_grad( 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"].detach()} def p_sample_loop( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, dump_steps=None, const_noise=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. :param const_noise: If True, will noise all samples with the same noise throughout sampling :return: a non-differentiable batch of samples. """ final = None if dump_steps is not None: dump = [] for i, sample in enumerate( 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, skip_timesteps=skip_timesteps, init_image=init_image, randomize_class=randomize_class, cond_fn_with_grad=cond_fn_with_grad, const_noise=const_noise, ) ): if dump_steps is not None and i in dump_steps: dump.append(deepcopy(sample["sample"])) final = sample if dump_steps is not None: return dump return final["sample"] def p_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, const_noise=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) if skip_timesteps and init_image is None: init_image = th.zeros_like(img) indices = list(range(self.num_timesteps - skip_timesteps))[::-1] if init_image is not None: my_t = th.ones([shape[0]], device=device, dtype=th.long) * indices[0] img = self.q_sample(init_image, my_t, img) if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices) # number of timestamps to diffuse for i in indices: t = th.tensor([i] * shape[0], device=device) if randomize_class and "y" in model_kwargs: model_kwargs["y"] = th.randint( low=0, high=model.num_classes, size=model_kwargs["y"].shape, device=model_kwargs["y"].device, ) with th.no_grad(): sample_fn = ( self.p_sample_with_grad if cond_fn_with_grad else self.p_sample ) out = sample_fn( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, const_noise=const_noise, ) yield out img = out["sample"] 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_orig = 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_orig, x, t, model_kwargs=model_kwargs ) else: out = out_orig # 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) ) 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_orig["pred_xstart"]} def ddim_sample_with_grad( 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(). """ with th.enable_grad(): x = x.detach().requires_grad_() out_orig = 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_with_grad( cond_fn, out_orig, x, t, model_kwargs=model_kwargs ) else: out = out_orig out["pred_xstart"] = out["pred_xstart"].detach() # 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_orig["pred_xstart"].detach()} 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, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, eta=0.0, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, dump_steps=None, const_noise=False, ): """ Generate samples from the model using DDIM. Same usage as p_sample_loop(). """ if dump_steps is not None: raise NotImplementedError() if const_noise == True: raise NotImplementedError() 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, skip_timesteps=skip_timesteps, init_image=init_image, randomize_class=randomize_class, cond_fn_with_grad=cond_fn_with_grad, ): final = sample return final["pred_xstart"] def ddim_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, eta=0.0, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, ): """ 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) if skip_timesteps and init_image is None: init_image = th.zeros_like(img) indices = list(range(self.num_timesteps - skip_timesteps))[::-1] if init_image is not None: my_t = th.ones([shape[0]], device=device, dtype=th.long) * indices[0] img = self.q_sample(init_image, my_t, img) 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) if randomize_class and "y" in model_kwargs: model_kwargs["y"] = th.randint( low=0, high=model.num_classes, size=model_kwargs["y"].shape, device=model_kwargs["y"].device, ) with th.no_grad(): sample_fn = ( self.ddim_sample_with_grad if cond_fn_with_grad else self.ddim_sample ) out = sample_fn( 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"] def plms_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, cond_fn_with_grad=False, order=2, old_out=None, ): """ Sample x_{t-1} from the model using Pseudo Linear Multistep. Same usage as p_sample(). """ if not int(order) or not 1 <= order <= 4: raise ValueError("order is invalid (should be int from 1-4).") def get_model_output(x, t): with th.set_grad_enabled(cond_fn_with_grad and cond_fn is not None): x = x.detach().requires_grad_() if cond_fn_with_grad else x out_orig = 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: if cond_fn_with_grad: out = self.condition_score_with_grad( cond_fn, out_orig, x, t, model_kwargs=model_kwargs ) x = x.detach() else: out = self.condition_score( cond_fn, out_orig, x, t, model_kwargs=model_kwargs ) else: out = out_orig # 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"]) return eps, out, out_orig alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape) alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t, x.shape) eps, out, out_orig = get_model_output(x, t) if order > 1 and old_out is None: # Pseudo Improved Euler old_eps = [eps] mean_pred = ( out["pred_xstart"] * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev) * eps ) eps_2, _, _ = get_model_output(mean_pred, t - 1) eps_prime = (eps + eps_2) / 2 pred_prime = self._predict_xstart_from_eps(x, t, eps_prime) mean_pred = ( pred_prime * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev) * eps_prime ) else: # Pseudo Linear Multistep (Adams-Bashforth) old_eps = old_out["old_eps"] old_eps.append(eps) cur_order = min(order, len(old_eps)) if cur_order == 1: eps_prime = old_eps[-1] elif cur_order == 2: eps_prime = (3 * old_eps[-1] - old_eps[-2]) / 2 elif cur_order == 3: eps_prime = (23 * old_eps[-1] - 16 * old_eps[-2] + 5 * old_eps[-3]) / 12 elif cur_order == 4: eps_prime = ( 55 * old_eps[-1] - 59 * old_eps[-2] + 37 * old_eps[-3] - 9 * old_eps[-4] ) / 24 else: raise RuntimeError("cur_order is invalid.") pred_prime = self._predict_xstart_from_eps(x, t, eps_prime) mean_pred = ( pred_prime * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev) * eps_prime ) if len(old_eps) >= order: old_eps.pop(0) nonzero_mask = (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) sample = mean_pred * nonzero_mask + out["pred_xstart"] * (1 - nonzero_mask) return { "sample": sample, "pred_xstart": out_orig["pred_xstart"], "old_eps": old_eps, } def plms_sample_loop( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, order=2, ): """ Generate samples from the model using Pseudo Linear Multistep. Same usage as p_sample_loop(). """ final = None for sample in self.plms_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, skip_timesteps=skip_timesteps, init_image=init_image, randomize_class=randomize_class, cond_fn_with_grad=cond_fn_with_grad, order=order, ): final = sample return final["sample"] def plms_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, skip_timesteps=0, init_image=None, randomize_class=False, cond_fn_with_grad=False, order=2, ): """ Use PLMS to sample from the model and yield intermediate samples from each timestep of PLMS. 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) if skip_timesteps and init_image is None: init_image = th.zeros_like(img) indices = list(range(self.num_timesteps - skip_timesteps))[::-1] if init_image is not None: my_t = th.ones([shape[0]], device=device, dtype=th.long) * indices[0] img = self.q_sample(init_image, my_t, img) if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices) old_out = None for i in indices: t = th.tensor([i] * shape[0], device=device) if randomize_class and "y" in model_kwargs: model_kwargs["y"] = th.randint( low=0, high=model.num_classes, size=model_kwargs["y"].shape, device=model_kwargs["y"].device, ) with th.no_grad(): out = self.plms_sample( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, cond_fn_with_grad=cond_fn_with_grad, order=order, old_out=old_out, ) yield out old_out = out img = out["sample"] 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 = 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"] ) 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"]} def training_losses(self, model, x_start, t, model_kwargs=None, noise=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. """ mask = model_kwargs["y"]["mask"] 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 ) # use the formula to diffuse the starting tensor by t steps terms = {} # set random dropout for conditioning in training model_kwargs["cond_drop_prob"] = 0.2 model_output = model(x_t, self._scale_timesteps(t), **model_kwargs) target = { ModelMeanType.PREVIOUS_X: self.q_posterior_mean_variance( x_start=x_start, x_t=x_t, t=t )[0], ModelMeanType.START_X: x_start, ModelMeanType.EPSILON: noise, }[self.model_mean_type] model_output = model_output.permute(0, 2, 1).unsqueeze(2) assert model_output.shape == target.shape == x_start.shape missing_mask = model_kwargs["y"]["missing"][..., 0] missing_mask = missing_mask.unsqueeze(1).unsqueeze(1) missing_mask = mask * missing_mask terms["rot_mse"] = self.masked_l2(target, model_output, missing_mask) if self.lambda_vel > 0.0: target_vel = target[..., 1:] - target[..., :-1] model_output_vel = model_output[..., 1:] - model_output[..., :-1] terms["vel_mse"] = self.masked_l2( target_vel, model_output_vel, mask[:, :, :, 1:], ) terms["loss"] = terms["rot_mse"] + (self.lambda_vel * terms.get("vel_mse", 0.0)) with torch.no_grad(): terms["vb"] = self._vb_terms_bpd( model, x_start, x_t, t, clip_denoised=False, model_kwargs=model_kwargs, )["output"] return terms 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)