import math import numpy as np import torch as th import enum from .diffusion_utils import discretized_gaussian_log_likelihood, normal_kl from ..utils.tools import assert_shape def mean_flat(tensor): """ Take the mean over all non-batch dimensions. """ return tensor.mean(dim=list(range(1, len(tensor.shape)))) 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 VELOCITY = enum.auto() # the model predicts v predict_type_dict = { "epsilon": ModelMeanType.EPSILON, "sample": ModelMeanType.START_X, "v_prediction": ModelMeanType.VELOCITY, } 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 def _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, warmup_frac): betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64) warmup_time = int(num_diffusion_timesteps * warmup_frac) betas[:warmup_time] = np.linspace( beta_start, beta_end, warmup_time, dtype=np.float64 ) return betas 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 == "quad": betas = ( np.linspace( beta_start**0.5, beta_end**0.5, num_diffusion_timesteps, dtype=np.float64, ) ** 2 ) elif beta_schedule == "linear": betas = np.linspace( beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64 ) elif beta_schedule == "warmup10": betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.1) elif beta_schedule == "warmup50": betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.5) elif beta_schedule == "const": betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64) elif beta_schedule == "jsd": # 1/T, 1/(T-1), 1/(T-2), ..., 1 betas = 1.0 / np.linspace( num_diffusion_timesteps, 1, num_diffusion_timesteps, dtype=np.float64 ) else: raise NotImplementedError(beta_schedule) assert_shape(betas, (num_diffusion_timesteps,)) return betas def get_named_beta_schedule( schedule_name, num_diffusion_timesteps, beta_start=0.0001, beta_end=0.02 ): """ 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 * beta_start, # DDPM beta_end=scale * beta_end, # DDPM num_diffusion_timesteps=num_diffusion_timesteps, # DDPM ) elif schedule_name == "scaled_linear": return get_beta_schedule( "quad", beta_start=beta_start, # StableDiffusion, should be 0.00085 beta_end=beta_end, # StableDiffusion, should be 0.012 num_diffusion_timesteps=num_diffusion_timesteps, # StableDiffusion ) elif schedule_name == "squaredcos_cap_v2": 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 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, mse_loss_weight_type="constant", noise_offset=0.0, ): 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.mse_loss_weight_type = mse_loss_weight_type self.noise_offset = noise_offset # Use float64 for accuracy. betas = np.array(betas, dtype=np.float64) alphas = 1.0 - betas alphas_cumprod = np.cumprod(alphas, axis=0) 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]) self.alphas_cumprod = alphas_cumprod 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_shape(self.alphas_cumprod_prev, (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:])) if len(self.posterior_variance) > 1 else np.array([]) ) 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.sampler = { "ddpm": self.p_sample_loop, "ddim": self.ddim_sample_loop, "plms": self.plms_sample_loop, } 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_shape(noise, x_start) 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_shape(x_start, x_t) 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_shape( posterior_mean.shape[:1], posterior_variance.shape[:1], posterior_log_variance_clipped.shape[:1], x_start.shape[:1], ) 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, model_var_type=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. :param model_var_type: if not None, overlap the default self.model_var_type. It is useful when training with learned var but sampling with fixed var. :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 = {} if model_var_type is None: model_var_type = self.model_var_type B, C = x.shape[:2] assert_shape(t, (B,)) out_dict = model(x, t, **model_kwargs) model_output = out_dict["x"] if len(out_dict) > 1: extra = {k: v for k, v in out_dict.items() if k != "x"} else: extra = None # self.model_var_type corresponds to model output if self.model_var_type in [ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE]: assert_shape(model_output, (B, C * 2, *x.shape[2:])) model_output, model_var_values = th.split(model_output, C, dim=1) # model_var_type corresponds to reverse diffusion process if model_var_type in [ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE]: if 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, ), }[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 == 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, ModelMeanType.VELOCITY, ]: if self.model_mean_type == ModelMeanType.START_X: pred_xstart = process_xstart(model_output) elif self.model_mean_type == ModelMeanType.EPSILON: pred_xstart = process_xstart( self._predict_xstart_from_eps(x_t=x, t=t, eps=model_output) ) else: pred_xstart = process_xstart( self._predict_xstart_from_v(x_t=x, t=t, v=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_shape(model_mean, model_log_variance, pred_xstart, x) 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_shape(x_t, eps) 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_v(self, x_t, t, v): assert_shape(x_t, v) return ( _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t - _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v ) def _predict_xstart_from_xprev(self, x_t, t, xprev): assert_shape(x_t, xprev) 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 _velocity_from_xstart_and_noise(self, x_start, t, noise): return ( _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * noise - _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start ) 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_shape(decoder_nll, x_start) 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, model_kwargs=None, controlnet=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 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 = {} # Time steps t = th.randint( 0, self.num_timesteps, (x_start.shape[0],), device=x_start.device ) # Noise if noise is None: noise = th.randn_like(x_start) if self.noise_offset > 0: # Add channel wise noise offset # https://www.crosslabs.org/blog/diffusion-with-offset-noise noise = noise + self.noise_offset * th.randn( *x_start.shape[:2], 1, 1, device=x_start.device ) x_t = self.q_sample(x_start, t, noise=noise) terms = {} if self.mse_loss_weight_type == "constant": mse_loss_weight = th.ones_like(t) elif self.mse_loss_weight_type.startswith("min_snr_"): alpha = _extract_into_tensor(self.sqrt_alphas_cumprod, t, t.shape) sigma = _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, t.shape) snr = (alpha / sigma) ** 2 k = float(self.mse_loss_weight_type.split("min_snr_")[-1]) # min{snr, k} mse_loss_weight = ( th.stack([snr, k * th.ones_like(t)], dim=1).min(dim=1)[0] / snr ) else: raise ValueError(self.mse_loss_weight_type) if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL: out_dict = 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"] = out_dict["output"] if self.loss_type == LossType.RESCALED_KL: terms["loss"] *= self.num_timesteps extra = out_dict["extra"] elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE: if controlnet != None: controls = controlnet(x_t, t, **model_kwargs) model_kwargs.pop("condition") model_kwargs.update(controls) out_dict = model(x_t, t, **model_kwargs) model_output = out_dict["x"] extra = {k: v for k, v in out_dict.items() if k != "x"} if self.model_var_type in [ ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE, ]: B, C = x_t.shape[:2] assert_shape(model_output, (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: dict(x=r), x_start=x_start, x_t=x_t, t=t, clip_denoised=False, )["output"] 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.VELOCITY: target = self._velocity_from_xstart_and_noise(x_start, t, noise) else: 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] assert_shape(model_output, target, x_start) raw_mse = mean_flat((target - model_output) ** 2).detach() terms["mse"] = mse_loss_weight * mean_flat((target - model_output) ** 2) if "vb" in terms: terms["loss"] = terms["mse"] + terms["vb"] terms["raw_loss"] = raw_mse + terms["vb"].detach() else: terms["loss"] = terms["mse"] terms["raw_loss"] = raw_mse else: raise NotImplementedError(self.loss_type) terms.update(extra) return terms 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) 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) 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, model_var_type=None, **kwargs, ): """ 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. :param model_var_type: if not None, overlap the default self.model_var_type. It is useful when training with learned var but sampling with fixed var. :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, model_var_type=model_var_type, ) 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=True, denoised_fn=None, cond_fn=None, model_kwargs=None, model_var_type=None, device=None, progress=False, progress_leave=True, **kwargs, ): """ 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 model_var_type: if not None, overlap the default self.model_var_type. It is useful when training with learned var but sampling with fixed var. :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, model_var_type=model_var_type, device=device, progress=progress, progress_leave=progress_leave, **kwargs, ): final = sample 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, model_var_type=None, device=None, progress=False, progress_leave=True, **kwargs, ): """ 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] if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices, leave=progress_leave) 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, model_var_type=model_var_type, **kwargs, ) 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 = 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=True, 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=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, progress_leave=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, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, device=device, progress=progress, progress_leave=progress_leave, eta=eta, ): final = sample return final["sample"] 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, progress_leave=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, leave=progress_leave) 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 out img = out["sample"] 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 = 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 get_eps( self, model, x, t, model_kwargs, cond_fn=None, ): model_output = model(x, t, **model_kwargs)["x"] if isinstance(model_output, tuple): model_output, _ = model_output eps = model_output[:, :4] if cond_fn is not None: alpha_bar = _extract_into_tensor_lerp(self.alphas_cumprod, t, x.shape) eps = eps - th.sqrt(1 - alpha_bar) * cond_fn(x, t, **model_kwargs) return eps def eps_to_pred_xstart( self, x, eps, t, ): alpha_bar = _extract_into_tensor_lerp(self.alphas_cumprod, t, x.shape) return (x - eps * th.sqrt(1 - alpha_bar)) / th.sqrt(alpha_bar) def pndm_transfer( self, x, eps, t_1, t_2, ): pred_xstart = self.eps_to_pred_xstart(x, eps, t_1) alpha_bar_prev = _extract_into_tensor_lerp(self.alphas_cumprod, t_2, x.shape) return pred_xstart * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev) * eps def prk_sample_loop( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, ): """ Generate samples from the model using PRK. Same usage as p_sample_loop(). """ final = None for sample in self.prk_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, ): final = sample return final["sample"] def prk_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, device=None, progress=False, ): """ Use PRK to sample from the model and yield intermediate samples from each timestep of PRK. 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][1:-1] if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices, leave=False) for i in indices: t = th.tensor([i] * shape[0], device=device) with th.no_grad(): out = self.prk_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"] def prk_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, ): """ Sample x_{t-1} from the model using fourth-order Pseudo Runge-Kutta (https://openreview.net/forum?id=PlKWVd2yBkY). Same usage as p_sample(). """ if model_kwargs is None: model_kwargs = {} def process_xstart(x): if denoised_fn is not None: x = denoised_fn(x) if clip_denoised: return x.clamp(-1, 1) return x eps_1 = self.get_eps(model, x, t, model_kwargs, cond_fn) x_1 = self.pndm_transfer(x, eps_1, t, t - 0.5) eps_2 = self.get_eps(model, x_1, t - 0.5, model_kwargs, cond_fn) x_2 = self.pndm_transfer(x, eps_2, t, t - 0.5) eps_3 = self.get_eps(model, x_2, t - 0.5, model_kwargs, cond_fn) x_3 = self.pndm_transfer(x, eps_3, t, t - 1) eps_4 = self.get_eps(model, x_3, t - 1, model_kwargs, cond_fn) eps_prime = (eps_1 + 2 * eps_2 + 2 * eps_3 + eps_4) / 6 sample = self.pndm_transfer(x, eps_prime, t, t - 1) pred_xstart = self.eps_to_pred_xstart(x, eps_prime, t) pred_xstart = process_xstart(pred_xstart) return {"sample": sample, "pred_xstart": pred_xstart, "eps": eps_prime} 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, progress_leave=True, ): """ Generate samples from the model using PLMS. Same usage as p_sample_loop(). """ assert ( self.model_mean_type == ModelMeanType.EPSILON ), "plms_sample only support model_mean_type == ModelMeanType.EPSILON" 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, progress_leave=progress_leave, ): 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, progress_leave=True, ): """ 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) indices = list(range(self.num_timesteps))[::-1][1:-1] if progress: # Lazy import so that we don't depend on tqdm. from tqdm.auto import tqdm indices = tqdm(indices, leave=progress_leave) old_eps = [] for i in indices: t = th.tensor([i] * shape[0], device=device) with th.no_grad(): if len(old_eps) < 3: out = self.prk_sample( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, ) else: out = self.plms_sample( model, img, old_eps, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, cond_fn=cond_fn, model_kwargs=model_kwargs, ) old_eps.pop(0) old_eps.append(out["eps"]) yield out img = out["sample"] def plms_sample( self, model, x, old_eps, t, clip_denoised=True, denoised_fn=None, cond_fn=None, model_kwargs=None, ): """ Sample x_{t-1} from the model using fourth-order Pseudo Linear Multistep (https://openreview.net/forum?id=PlKWVd2yBkY). """ if model_kwargs is None: model_kwargs = {} def process_xstart(x): if denoised_fn is not None: x = denoised_fn(x) if clip_denoised: return x.clamp(-1, 1) return x eps = self.get_eps(model, x, t, model_kwargs, cond_fn) eps_prime = ( 55 * eps - 59 * old_eps[-1] + 37 * old_eps[-2] - 9 * old_eps[-3] ) / 24 sample = self.pndm_transfer(x, eps_prime, t, t - 1) pred_xstart = self.eps_to_pred_xstart(x, eps, t) pred_xstart = process_xstart(pred_xstart) return {"sample": sample, "pred_xstart": pred_xstart, "eps": eps} 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 _extract_into_tensor_lerp(arr, timesteps, broadcast_shape): """ Extract values from arr with fractional time steps """ timesteps = timesteps.float() frac = timesteps.frac() while len(frac.shape) < len(broadcast_shape): frac = frac[..., None] res_1 = _extract_into_tensor(arr, timesteps.floor().long(), broadcast_shape) res_2 = _extract_into_tensor(arr, timesteps.ceil().long(), broadcast_shape) return th.lerp(res_1, res_2, frac)