910 lines
34 KiB
Python
910 lines
34 KiB
Python
"""
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This code started out as a PyTorch port of Ho et al's diffusion models:
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https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py
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Docstrings have been added, as well as DDIM sampling and a new collection of beta schedules.
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"""
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import enum
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import math
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import numpy as np
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import torch
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import torch as th
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from tqdm import tqdm
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from .nn import mean_flat
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from .losses import normal_kl, discretized_gaussian_log_likelihood
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def get_named_beta_schedule(schedule_name, num_diffusion_timesteps):
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"""
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Get a pre-defined beta schedule for the given name.
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The beta schedule library consists of beta schedules which remain similar
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in the limit of num_diffusion_timesteps.
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Beta schedules may be added, but should not be removed or changed once
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they are committed to maintain backwards compatibility.
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"""
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if schedule_name == "linear":
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# Linear schedule from Ho et al, extended to work for any number of
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# diffusion steps.
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scale = 1000 / num_diffusion_timesteps
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beta_start = scale * 0.0001
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beta_end = scale * 0.02
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return np.linspace(
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beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64
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)
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elif schedule_name == "cosine":
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return betas_for_alpha_bar(
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num_diffusion_timesteps,
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lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2,
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)
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else:
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raise NotImplementedError(f"unknown beta schedule: {schedule_name}")
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def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):
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"""
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Create a beta schedule that discretizes the given alpha_t_bar function,
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which defines the cumulative product of (1-beta) over time from t = [0,1].
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:param num_diffusion_timesteps: the number of betas to produce.
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:param alpha_bar: a lambda that takes an argument t from 0 to 1 and
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produces the cumulative product of (1-beta) up to that
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part of the diffusion process.
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:param max_beta: the maximum beta to use; use values lower than 1 to
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prevent singularities.
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"""
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betas = []
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for i in range(num_diffusion_timesteps):
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t1 = i / num_diffusion_timesteps
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t2 = (i + 1) / num_diffusion_timesteps
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betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
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return np.array(betas)
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class ModelMeanType(enum.Enum):
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"""
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Which type of output the model predicts.
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"""
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PREVIOUS_X = 'previous_x' # the model predicts x_{t-1}
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START_X = 'start_x' # the model predicts x_0
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EPSILON = 'epsilon' # the model predicts epsilon
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class ModelVarType(enum.Enum):
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"""
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What is used as the model's output variance.
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The LEARNED_RANGE option has been added to allow the model to predict
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values between FIXED_SMALL and FIXED_LARGE, making its job easier.
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"""
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LEARNED = 'learned'
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FIXED_SMALL = 'fixed_small'
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FIXED_LARGE = 'fixed_large'
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LEARNED_RANGE = 'learned_range'
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class LossType(enum.Enum):
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MSE = 'mse' # use raw MSE loss (and KL when learning variances)
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RESCALED_MSE = 'rescaled_mse' # use raw MSE loss (with RESCALED_KL when learning variances)
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KL = 'kl' # use the variational lower-bound
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RESCALED_KL = 'rescaled_kl' # like KL, but rescale to estimate the full VLB
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def is_vb(self):
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return self == LossType.KL or self == LossType.RESCALED_KL
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class GaussianDiffusion:
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"""
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Utilities for training and sampling diffusion models.
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Ported directly from here, and then adapted over time to further experimentation.
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https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42
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:param betas: a 1-D numpy array of betas for each diffusion timestep,
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starting at T and going to 1.
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:param model_mean_type: a ModelMeanType determining what the model outputs.
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:param model_var_type: a ModelVarType determining how variance is output.
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:param loss_type: a LossType determining the loss function to use.
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:param rescale_timesteps: if True, pass floating point timesteps into the
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model so that they are always scaled like in the
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original paper (0 to 1000).
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"""
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def __init__(
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self,
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*,
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betas,
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model_mean_type,
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model_var_type,
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loss_type,
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rescale_timesteps=False,
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):
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self.model_mean_type = ModelMeanType(model_mean_type)
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self.model_var_type = ModelVarType(model_var_type)
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self.loss_type = LossType(loss_type)
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self.rescale_timesteps = rescale_timesteps
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# Use float64 for accuracy.
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betas = np.array(betas, dtype=np.float64)
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self.betas = betas
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assert len(betas.shape) == 1, "betas must be 1-D"
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assert (betas > 0).all() and (betas <= 1).all()
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self.num_timesteps = int(betas.shape[0])
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alphas = 1.0 - betas
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self.alphas_cumprod = np.cumprod(alphas, axis=0)
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self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1])
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self.alphas_cumprod_next = np.append(self.alphas_cumprod[1:], 0.0)
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assert self.alphas_cumprod_prev.shape == (self.num_timesteps,)
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# calculations for diffusion q(x_t | x_{t-1}) and others
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self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod)
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self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod)
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self.log_one_minus_alphas_cumprod = np.log(1.0 - self.alphas_cumprod)
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self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod)
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self.sqrt_recipm1_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod - 1)
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# calculations for posterior q(x_{t-1} | x_t, x_0)
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self.posterior_variance = (
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betas * (1.0 - self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod)
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)
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# log calculation clipped because the posterior variance is 0 at the
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# beginning of the diffusion chain.
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self.posterior_log_variance_clipped = np.log(
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np.append(self.posterior_variance[1], self.posterior_variance[1:])
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)
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self.posterior_mean_coef1 = (
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betas * np.sqrt(self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod)
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)
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self.posterior_mean_coef2 = (
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(1.0 - self.alphas_cumprod_prev)
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* np.sqrt(alphas)
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/ (1.0 - self.alphas_cumprod)
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)
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def q_mean_variance(self, x_start, t):
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"""
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Get the distribution q(x_t | x_0).
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:param x_start: the [N x C x ...] tensor of noiseless inputs.
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:param t: the number of diffusion steps (minus 1). Here, 0 means one step.
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:return: A tuple (mean, variance, log_variance), all of x_start's shape.
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"""
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mean = (
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_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
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)
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variance = _extract_into_tensor(1.0 - self.alphas_cumprod, t, x_start.shape)
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log_variance = _extract_into_tensor(
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self.log_one_minus_alphas_cumprod, t, x_start.shape
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)
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return mean, variance, log_variance
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def q_sample(self, x_start, t, noise=None):
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"""
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Diffuse the data for a given number of diffusion steps.
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In other words, sample from q(x_t | x_0).
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:param x_start: the initial data batch.
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:param t: the number of diffusion steps (minus 1). Here, 0 means one step.
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:param noise: if specified, the split-out normal noise.
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:return: A noisy version of x_start.
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"""
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if noise is None:
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noise = th.randn_like(x_start)
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assert noise.shape == x_start.shape
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return (
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_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
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+ _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape)
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* noise
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)
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def q_posterior_mean_variance(self, x_start, x_t, t):
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"""
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Compute the mean and variance of the diffusion posterior:
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q(x_{t-1} | x_t, x_0)
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"""
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assert x_start.shape == x_t.shape
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posterior_mean = (
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_extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) * x_start
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+ _extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) * x_t
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)
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posterior_variance = _extract_into_tensor(self.posterior_variance, t, x_t.shape)
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posterior_log_variance_clipped = _extract_into_tensor(
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self.posterior_log_variance_clipped, t, x_t.shape
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)
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assert (
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posterior_mean.shape[0]
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== posterior_variance.shape[0]
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== posterior_log_variance_clipped.shape[0]
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== x_start.shape[0]
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)
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return posterior_mean, posterior_variance, posterior_log_variance_clipped
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def p_mean_variance(
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self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None
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):
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"""
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Apply the model to get p(x_{t-1} | x_t), as well as a prediction of
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the initial x, x_0.
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:param model: the model, which takes a signal and a batch of timesteps
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as input.
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:param x: the [N x C x ...] tensor at time t.
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:param t: a 1-D Tensor of timesteps.
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:param clip_denoised: if True, clip the denoised signal into [-1, 1].
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:param denoised_fn: if not None, a function which applies to the
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x_start prediction before it is used to sample. Applies before
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clip_denoised.
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:param model_kwargs: if not None, a dict of extra keyword arguments to
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pass to the model. This can be used for conditioning.
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:return: a dict with the following keys:
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- 'mean': the model mean output.
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- 'variance': the model variance output.
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- 'log_variance': the log of 'variance'.
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- 'pred_xstart': the prediction for x_0.
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"""
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if model_kwargs is None:
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model_kwargs = {}
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B, C = x.shape[:2]
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assert t.shape == (B,)
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model_output = model(x, self._scale_timesteps(t), **model_kwargs)
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if self.model_var_type in [ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE]:
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assert model_output.shape == (B, C * 2, *x.shape[2:])
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model_output, model_var_values = th.split(model_output, C, dim=1)
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if self.model_var_type == ModelVarType.LEARNED:
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model_log_variance = model_var_values
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model_variance = th.exp(model_log_variance)
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else:
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min_log = _extract_into_tensor(
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self.posterior_log_variance_clipped, t, x.shape
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)
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max_log = _extract_into_tensor(np.log(self.betas), t, x.shape)
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# The model_var_values is [-1, 1] for [min_var, max_var].
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frac = (model_var_values + 1) / 2
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model_log_variance = frac * max_log + (1 - frac) * min_log
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model_variance = th.exp(model_log_variance)
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else:
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model_variance, model_log_variance = {
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# for fixedlarge, we set the initial (log-)variance like so
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# to get a better decoder log likelihood.
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ModelVarType.FIXED_LARGE: (
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np.append(self.posterior_variance[1], self.betas[1:]),
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np.log(np.append(self.posterior_variance[1], self.betas[1:])),
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),
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ModelVarType.FIXED_SMALL: (
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self.posterior_variance,
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self.posterior_log_variance_clipped,
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),
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}[self.model_var_type]
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model_variance = _extract_into_tensor(model_variance, t, x.shape)
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model_log_variance = _extract_into_tensor(model_log_variance, t, x.shape)
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def process_xstart(x):
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if denoised_fn is not None:
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x = denoised_fn(x)
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if clip_denoised:
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return x.clamp(-1, 1)
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return x
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if self.model_mean_type == ModelMeanType.PREVIOUS_X:
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pred_xstart = process_xstart(
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self._predict_xstart_from_xprev(x_t=x, t=t, xprev=model_output)
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)
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model_mean = model_output
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elif self.model_mean_type in [ModelMeanType.START_X, ModelMeanType.EPSILON]:
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if self.model_mean_type == ModelMeanType.START_X:
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pred_xstart = process_xstart(model_output)
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else:
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pred_xstart = process_xstart(
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self._predict_xstart_from_eps(x_t=x, t=t, eps=model_output)
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)
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model_mean, _, _ = self.q_posterior_mean_variance(
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x_start=pred_xstart, x_t=x, t=t
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)
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else:
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raise NotImplementedError(self.model_mean_type)
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assert (
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model_mean.shape == model_log_variance.shape == pred_xstart.shape == x.shape
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)
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return {
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"mean": model_mean,
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"variance": model_variance,
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"log_variance": model_log_variance,
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"pred_xstart": pred_xstart,
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}
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def _predict_xstart_from_eps(self, x_t, t, eps):
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assert x_t.shape == eps.shape
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return (
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_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t
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- _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * eps
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)
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def _predict_xstart_from_xprev(self, x_t, t, xprev):
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assert x_t.shape == xprev.shape
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return ( # (xprev - coef2*x_t) / coef1
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_extract_into_tensor(1.0 / self.posterior_mean_coef1, t, x_t.shape) * xprev
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- _extract_into_tensor(
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self.posterior_mean_coef2 / self.posterior_mean_coef1, t, x_t.shape
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)
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* x_t
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)
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def _predict_eps_from_xstart(self, x_t, t, pred_xstart):
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return (
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_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t
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- pred_xstart
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) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
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def _scale_timesteps(self, t):
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if self.rescale_timesteps:
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return t.float() * (1000.0 / self.num_timesteps)
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return t
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def condition_mean(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
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"""
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Compute the mean for the previous step, given a function cond_fn that
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computes the gradient of a conditional log probability with respect to
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x. In particular, cond_fn computes grad(log(p(y|x))), and we want to
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condition on y.
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This uses the conditioning strategy from Sohl-Dickstein et al. (2015).
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"""
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gradient = cond_fn(x, self._scale_timesteps(t), **model_kwargs)
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new_mean = (
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p_mean_var["mean"].float() + p_mean_var["variance"] * gradient.float()
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)
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return new_mean
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def condition_score(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
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"""
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Compute what the p_mean_variance output would have been, should the
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model's score function be conditioned by cond_fn.
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See condition_mean() for details on cond_fn.
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Unlike condition_mean(), this instead uses the conditioning strategy
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from Song et al (2020).
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"""
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alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
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eps = self._predict_eps_from_xstart(x, t, p_mean_var["pred_xstart"])
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eps = eps - (1 - alpha_bar).sqrt() * cond_fn(
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x, self._scale_timesteps(t), **model_kwargs
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)
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out = p_mean_var.copy()
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out["pred_xstart"] = self._predict_xstart_from_eps(x, t, eps)
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out["mean"], _, _ = self.q_posterior_mean_variance(
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x_start=out["pred_xstart"], x_t=x, t=t
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)
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return out
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def p_sample(
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self,
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model,
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x,
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t,
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clip_denoised=True,
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denoised_fn=None,
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cond_fn=None,
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model_kwargs=None,
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):
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"""
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Sample x_{t-1} from the model at the given timestep.
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:param model: the model to sample from.
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:param x: the current tensor at x_{t-1}.
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:param t: the value of t, starting at 0 for the first diffusion step.
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:param clip_denoised: if True, clip the x_start prediction to [-1, 1].
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:param denoised_fn: if not None, a function which applies to the
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x_start prediction before it is used to sample.
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:param cond_fn: if not None, this is a gradient function that acts
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similarly to the model.
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:param model_kwargs: if not None, a dict of extra keyword arguments to
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pass to the model. This can be used for conditioning.
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:return: a dict containing the following keys:
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- 'sample': a random sample from the model.
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- 'pred_xstart': a prediction of x_0.
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"""
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out = self.p_mean_variance(
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model,
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x,
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t,
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clip_denoised=clip_denoised,
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denoised_fn=denoised_fn,
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model_kwargs=model_kwargs,
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)
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noise = th.randn_like(x)
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nonzero_mask = (
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(t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
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) # no noise when t == 0
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if cond_fn is not None:
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out["mean"] = self.condition_mean(
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cond_fn, out, x, t, model_kwargs=model_kwargs
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)
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sample = out["mean"] + nonzero_mask * th.exp(0.5 * out["log_variance"]) * noise
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|
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,
|
|
device=None,
|
|
progress=False,
|
|
):
|
|
"""
|
|
Generate samples from the model.
|
|
|
|
:param model: the model module.
|
|
:param shape: the shape of the samples, (N, C, H, W).
|
|
:param noise: if specified, the noise from the encoder to sample.
|
|
Should be of the same shape as `shape`.
|
|
:param clip_denoised: if True, clip x_start predictions to [-1, 1].
|
|
:param denoised_fn: if not None, a function which applies to the
|
|
x_start prediction before it is used to sample.
|
|
:param cond_fn: if not None, this is a gradient function that acts
|
|
similarly to the model.
|
|
:param model_kwargs: if not None, a dict of extra keyword arguments to
|
|
pass to the model. This can be used for conditioning.
|
|
:param device: if specified, the device to create the samples on.
|
|
If not specified, use a model parameter's device.
|
|
:param progress: if True, show a tqdm progress bar.
|
|
:return: a non-differentiable batch of samples.
|
|
"""
|
|
final = None
|
|
for sample in self.p_sample_loop_progressive(
|
|
model,
|
|
shape,
|
|
noise=noise,
|
|
clip_denoised=clip_denoised,
|
|
denoised_fn=denoised_fn,
|
|
cond_fn=cond_fn,
|
|
model_kwargs=model_kwargs,
|
|
device=device,
|
|
progress=progress,
|
|
):
|
|
final = sample
|
|
return final["sample"]
|
|
|
|
def p_sample_loop_progressive(
|
|
self,
|
|
model,
|
|
shape,
|
|
noise=None,
|
|
clip_denoised=True,
|
|
denoised_fn=None,
|
|
cond_fn=None,
|
|
model_kwargs=None,
|
|
device=None,
|
|
progress=False,
|
|
):
|
|
"""
|
|
Generate samples from the model and yield intermediate samples from
|
|
each timestep of diffusion.
|
|
|
|
Arguments are the same as p_sample_loop().
|
|
Returns a generator over dicts, where each dict is the return value of
|
|
p_sample().
|
|
"""
|
|
if device is None:
|
|
device = next(model.parameters()).device
|
|
assert isinstance(shape, (tuple, list))
|
|
if noise is not None:
|
|
img = noise
|
|
else:
|
|
img = th.randn(*shape, device=device)
|
|
indices = list(range(self.num_timesteps))[::-1]
|
|
|
|
for i in tqdm(indices):
|
|
t = th.tensor([i] * shape[0], device=device)
|
|
with th.no_grad():
|
|
out = self.p_sample(
|
|
model,
|
|
img,
|
|
t,
|
|
clip_denoised=clip_denoised,
|
|
denoised_fn=denoised_fn,
|
|
cond_fn=cond_fn,
|
|
model_kwargs=model_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,
|
|
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,
|
|
):
|
|
"""
|
|
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,
|
|
):
|
|
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,
|
|
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)
|
|
|
|
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 _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.
|
|
"""
|
|
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 == LossType.KL or self.loss_type == LossType.RESCALED_KL:
|
|
terms["loss"] = self._vb_terms_bpd(
|
|
model=model,
|
|
x_start=x_start,
|
|
x_t=x_t,
|
|
t=t,
|
|
clip_denoised=False,
|
|
model_kwargs=model_kwargs,
|
|
)["output"]
|
|
if self.loss_type == LossType.RESCALED_KL:
|
|
terms["loss"] *= self.num_timesteps
|
|
elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE:
|
|
model_output = model(x_t, self._scale_timesteps(t), **model_kwargs)
|
|
|
|
if self.model_var_type in [
|
|
ModelVarType.LEARNED,
|
|
ModelVarType.LEARNED_RANGE,
|
|
]:
|
|
B, C = x_t.shape[:2]
|
|
assert model_output.shape == (B, C * 2, *x_t.shape[2:])
|
|
model_output, model_var_values = th.split(model_output, C, dim=1)
|
|
# Learn the variance using the variational bound, but don't let
|
|
# it affect our mean prediction.
|
|
frozen_out = th.cat([model_output.detach(), model_var_values], dim=1)
|
|
terms["vb"] = self._vb_terms_bpd(
|
|
model=lambda *args, r=frozen_out: r,
|
|
x_start=x_start,
|
|
x_t=x_t,
|
|
t=t,
|
|
clip_denoised=False,
|
|
)["output"]
|
|
if self.loss_type == LossType.RESCALED_MSE:
|
|
# Divide by 1000 for equivalence with initial implementation.
|
|
# Without a factor of 1/1000, the VB term hurts the MSE term.
|
|
terms["vb"] *= self.num_timesteps / 1000.0
|
|
|
|
if self.model_mean_type == ModelMeanType.PREVIOUS_X:
|
|
target = self.q_posterior_mean_variance(
|
|
x_start=x_start, x_t=x_t, t=t
|
|
)[0]
|
|
x_start_pred = torch.zeros(x_start) # Not supported.
|
|
elif self.model_mean_type == ModelMeanType.START_X:
|
|
target = x_start
|
|
x_start_pred = model_output
|
|
elif self.model_mean_type == ModelMeanType.EPSILON:
|
|
target = noise
|
|
x_start_pred = self._predict_xstart_from_eps(x_t, t, model_output)
|
|
else:
|
|
raise NotImplementedError(self.model_mean_type)
|
|
assert model_output.shape == target.shape == x_start.shape
|
|
terms["mse"] = mean_flat((target - model_output) ** 2)
|
|
terms["x_start_predicted"] = x_start_pred
|
|
if "vb" in terms:
|
|
terms["loss"] = terms["mse"] + terms["vb"]
|
|
else:
|
|
terms["loss"] = terms["mse"]
|
|
else:
|
|
raise NotImplementedError(self.loss_type)
|
|
|
|
return terms
|
|
|
|
def _prior_bpd(self, x_start):
|
|
"""
|
|
Get the prior KL term for the variational lower-bound, measured in
|
|
bits-per-dim.
|
|
|
|
This term can't be optimized, as it only depends on the encoder.
|
|
|
|
:param x_start: the [N x C x ...] tensor of inputs.
|
|
:return: a batch of [N] KL values (in bits), one per batch element.
|
|
"""
|
|
batch_size = x_start.shape[0]
|
|
t = th.tensor([self.num_timesteps - 1] * batch_size, device=x_start.device)
|
|
qt_mean, _, qt_log_variance = self.q_mean_variance(x_start, t)
|
|
kl_prior = normal_kl(
|
|
mean1=qt_mean, logvar1=qt_log_variance, mean2=0.0, logvar2=0.0
|
|
)
|
|
return mean_flat(kl_prior) / np.log(2.0)
|
|
|
|
def calc_bpd_loop(self, model, x_start, clip_denoised=True, model_kwargs=None):
|
|
"""
|
|
Compute the entire variational lower-bound, measured in bits-per-dim,
|
|
as well as other related quantities.
|
|
|
|
:param model: the model to evaluate loss on.
|
|
:param x_start: the [N x C x ...] tensor of inputs.
|
|
:param clip_denoised: if True, clip denoised samples.
|
|
:param model_kwargs: if not None, a dict of extra keyword arguments to
|
|
pass to the model. This can be used for conditioning.
|
|
|
|
:return: a dict containing the following keys:
|
|
- total_bpd: the total variational lower-bound, per batch element.
|
|
- prior_bpd: the prior term in the lower-bound.
|
|
- vb: an [N x T] tensor of terms in the lower-bound.
|
|
- xstart_mse: an [N x T] tensor of x_0 MSEs for each timestep.
|
|
- mse: an [N x T] tensor of epsilon MSEs for each timestep.
|
|
"""
|
|
device = x_start.device
|
|
batch_size = x_start.shape[0]
|
|
|
|
vb = []
|
|
xstart_mse = []
|
|
mse = []
|
|
for t in list(range(self.num_timesteps))[::-1]:
|
|
t_batch = th.tensor([t] * batch_size, device=device)
|
|
noise = th.randn_like(x_start)
|
|
x_t = self.q_sample(x_start=x_start, t=t_batch, noise=noise)
|
|
# Calculate VLB term at the current timestep
|
|
with th.no_grad():
|
|
out = self._vb_terms_bpd(
|
|
model,
|
|
x_start=x_start,
|
|
x_t=x_t,
|
|
t=t_batch,
|
|
clip_denoised=clip_denoised,
|
|
model_kwargs=model_kwargs,
|
|
)
|
|
vb.append(out["output"])
|
|
xstart_mse.append(mean_flat((out["pred_xstart"] - x_start) ** 2))
|
|
eps = self._predict_eps_from_xstart(x_t, t_batch, out["pred_xstart"])
|
|
mse.append(mean_flat((eps - noise) ** 2))
|
|
|
|
vb = th.stack(vb, dim=1)
|
|
xstart_mse = th.stack(xstart_mse, dim=1)
|
|
mse = th.stack(mse, dim=1)
|
|
|
|
prior_bpd = self._prior_bpd(x_start)
|
|
total_bpd = vb.sum(dim=1) + prior_bpd
|
|
return {
|
|
"total_bpd": total_bpd,
|
|
"prior_bpd": prior_bpd,
|
|
"vb": vb,
|
|
"xstart_mse": xstart_mse,
|
|
"mse": mse,
|
|
}
|
|
|
|
|
|
def _extract_into_tensor(arr, timesteps, broadcast_shape):
|
|
"""
|
|
Extract values from a 1-D numpy array for a batch of indices.
|
|
|
|
:param arr: the 1-D numpy array.
|
|
:param timesteps: a tensor of indices into the array to extract.
|
|
:param broadcast_shape: a larger shape of K dimensions with the batch
|
|
dimension equal to the length of timesteps.
|
|
:return: a tensor of shape [batch_size, 1, ...] where the shape has K dims.
|
|
"""
|
|
res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float()
|
|
while len(res.shape) < len(broadcast_shape):
|
|
res = res[..., None]
|
|
return res.expand(broadcast_shape)
|