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7.6 KiB
Python

from math import sqrt
from random import random
import torch
from torch import nn, einsum
import torch.nn.functional as F
from tqdm import tqdm
from einops import rearrange, repeat, reduce
# helpers
def exists(val):
return val is not None
def default(val, d):
if exists(val):
return val
return d() if callable(d) else d
# tensor helpers
def log(t, eps = 1e-20):
return torch.log(t.clamp(min = eps))
# normalization functions
def normalize_to_neg_one_to_one(img):
return img * 2 - 1
def unnormalize_to_zero_to_one(t):
return (t + 1) * 0.5
# main class
class ElucidatedDiffusion(nn.Module):
def __init__(
self,
net,
*,
image_size,
channels = 3,
num_sample_steps = 32, # number of sampling steps
sigma_min = 0.002, # min noise level
sigma_max = 80, # max noise level
sigma_data = 0.5, # standard deviation of data distribution
rho = 7, # controls the sampling schedule
P_mean = -1.2, # mean of log-normal distribution from which noise is drawn for training
P_std = 1.2, # standard deviation of log-normal distribution from which noise is drawn for training
S_churn = 80, # parameters for stochastic sampling - depends on dataset, Table 5 in apper
S_tmin = 0.05,
S_tmax = 50,
S_noise = 1.003,
):
super().__init__()
assert net.random_or_learned_sinusoidal_cond
self.self_condition = net.self_condition
self.net = net
# image dimensions
self.channels = channels
self.image_size = image_size
# parameters
self.sigma_min = sigma_min
self.sigma_max = sigma_max
self.sigma_data = sigma_data
self.rho = rho
self.P_mean = P_mean
self.P_std = P_std
self.num_sample_steps = num_sample_steps # otherwise known as N in the paper
self.S_churn = S_churn
self.S_tmin = S_tmin
self.S_tmax = S_tmax
self.S_noise = S_noise
@property
def device(self):
return next(self.net.parameters()).device
# derived preconditioning params - Table 1
def c_skip(self, sigma):
return (self.sigma_data ** 2) / (sigma ** 2 + self.sigma_data ** 2)
def c_out(self, sigma):
return sigma * self.sigma_data * (self.sigma_data ** 2 + sigma ** 2) ** -0.5
def c_in(self, sigma):
return 1 * (sigma ** 2 + self.sigma_data ** 2) ** -0.5
def c_noise(self, sigma):
return log(sigma) * 0.25
# preconditioned network output
# equation (7) in the paper
def preconditioned_network_forward(self, noised_images, sigma, self_cond = None, clamp = False):
batch, device = noised_images.shape[0], noised_images.device
if isinstance(sigma, float):
sigma = torch.full((batch,), sigma, device = device)
padded_sigma = rearrange(sigma, 'b -> b 1 1 1')
net_out = self.net(
self.c_in(padded_sigma) * noised_images,
self.c_noise(sigma),
self_cond
)
out = self.c_skip(padded_sigma) * noised_images + self.c_out(padded_sigma) * net_out
if clamp:
out = out.clamp(-1., 1.)
return out
# sampling
# sample schedule
# equation (5) in the paper
def sample_schedule(self, num_sample_steps = None):
num_sample_steps = default(num_sample_steps, self.num_sample_steps)
N = num_sample_steps
inv_rho = 1 / self.rho
steps = torch.arange(num_sample_steps, device = self.device, dtype = torch.float32)
sigmas = (self.sigma_max ** inv_rho + steps / (N - 1) * (self.sigma_min ** inv_rho - self.sigma_max ** inv_rho)) ** self.rho
sigmas = F.pad(sigmas, (0, 1), value = 0.) # last step is sigma value of 0.
return sigmas
@torch.no_grad()
def sample(self, batch_size = 16, num_sample_steps = None, clamp = True):
num_sample_steps = default(num_sample_steps, self.num_sample_steps)
shape = (batch_size, self.channels, self.image_size, self.image_size)
# get the schedule, which is returned as (sigma, gamma) tuple, and pair up with the next sigma and gamma
sigmas = self.sample_schedule(num_sample_steps)
gammas = torch.where(
(sigmas >= self.S_tmin) & (sigmas <= self.S_tmax),
min(self.S_churn / num_sample_steps, sqrt(2) - 1),
0.
)
sigmas_and_gammas = list(zip(sigmas[:-1], sigmas[1:], gammas[:-1]))
# images is noise at the beginning
init_sigma = sigmas[0]
images = init_sigma * torch.randn(shape, device = self.device)
# for self conditioning
x_start = None
# gradually denoise
for sigma, sigma_next, gamma in tqdm(sigmas_and_gammas, desc = 'sampling time step'):
sigma, sigma_next, gamma = map(lambda t: t.item(), (sigma, sigma_next, gamma))
eps = self.S_noise * torch.randn(shape, device = self.device) # stochastic sampling
sigma_hat = sigma + gamma * sigma
images_hat = images + sqrt(sigma_hat ** 2 - sigma ** 2) * eps
self_cond = x_start if self.self_condition else None
model_output = self.preconditioned_network_forward(images_hat, sigma_hat, self_cond, clamp = clamp)
denoised_over_sigma = (images_hat - model_output) / sigma_hat
images_next = images_hat + (sigma_next - sigma_hat) * denoised_over_sigma
# second order correction, if not the last timestep
if sigma_next != 0:
self_cond = model_output if self.self_condition else None
model_output_next = self.preconditioned_network_forward(images_next, sigma_next, self_cond, clamp = clamp)
denoised_prime_over_sigma = (images_next - model_output_next) / sigma_next
images_next = images_hat + 0.5 * (sigma_next - sigma_hat) * (denoised_over_sigma + denoised_prime_over_sigma)
images = images_next
x_start = model_output
images = images.clamp(-1., 1.)
return unnormalize_to_zero_to_one(images)
# training
def loss_weight(self, sigma):
return (sigma ** 2 + self.sigma_data ** 2) * (sigma * self.sigma_data) ** -2
def noise_distribution(self, batch_size):
return (self.P_mean + self.P_std * torch.randn((batch_size,), device = self.device)).exp()
def forward(self, images):
batch_size, c, h, w, device, image_size, channels = *images.shape, images.device, self.image_size, self.channels
assert h == image_size and w == image_size, f'height and width of image must be {image_size}'
assert c == channels, 'mismatch of image channels'
images = normalize_to_neg_one_to_one(images)
sigmas = self.noise_distribution(batch_size)
padded_sigmas = rearrange(sigmas, 'b -> b 1 1 1')
noise = torch.randn_like(images)
noised_images = images + padded_sigmas * noise # alphas are 1. in the paper
self_cond = None
if self.self_condition and random() < 0.5:
# from hinton's group's bit diffusion paper
with torch.no_grad():
self_cond = self.preconditioned_network_forward(noised_images, sigmas)
self_cond.detach_()
denoised = self.preconditioned_network_forward(noised_images, sigmas, self_cond)
losses = F.mse_loss(denoised, images, reduction = 'none')
losses = reduce(losses, 'b ... -> b', 'mean')
losses = losses * self.loss_weight(sigmas)
return losses.mean()