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"""Adapted from https://github.com/lucidrains/denoising-diffusion-pytorch"""
from argparse import Namespace
import math
from typing import List, Tuple, Optional
import torch
import torch.nn.functional as F
from einops import reduce, rearrange
from torch import nn, Tensor
from models.unet_model import Unet
from trainers.utils import default, get_index_from_list, normalize_to_neg_one_to_one
def linear_beta_schedule(
timesteps: int,
start: float = 0.0001,
end: float = 0.02
) -> Tensor:
"""
:param timesteps: Number of time steps
:return schedule: betas at every timestep, (timesteps,)
"""
scale = 1000 / timesteps
beta_start = scale * start
beta_end = scale * end
return torch.linspace(beta_start, beta_end, timesteps, dtype=torch.float32)
def cosine_beta_schedule(timesteps: int, s: float = 0.008) -> Tensor:
"""
cosine schedule
as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
:param timesteps: Number of time steps
:param s: scaling factor
:return schedule: betas at every timestep, (timesteps,)
"""
steps = timesteps + 1
x = torch.linspace(0, timesteps, steps, dtype=torch.float32)
alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
return torch.clip(betas, 0, 0.999)
class DiffusionModel(nn.Module):
def __init__(self, config: Namespace):
super().__init__()
# Default parameters
self.config = config
dim: int = self.default('dim', 64)
dim_mults: List[int] = self.default('dim_mults', [1, 2, 4, 8])
channels: int = self.default('channels', 1)
timesteps: int = self.default('timesteps', 1000)
beta_schedule: str = self.default('beta_schedule', 'cosine')
objective: str = self.default('objective', 'pred_noise') # 'pred_noise' or 'pred_x_0'
p2_loss_weight_gamma: float = self.default('p2_loss_weight_gamma', 0.) # p2 loss weight, from https://arxiv.org/abs/2204.00227 - 0 is equivalent to weight of 1 across time - 1. is recommended
p2_loss_weight_k: float = self.default('p2_loss_weight_k', 1.)
dynamic_threshold_percentile: float = self.default('dynamic_threshold_percentile', 0.995)
self.timesteps = timesteps
self.objective = objective
self.dynamic_threshold_percentile = dynamic_threshold_percentile
self.model = Unet(
dim,
dim_mults=dim_mults,
channels=channels
)
if beta_schedule == 'linear':
betas = linear_beta_schedule(timesteps)
elif beta_schedule == 'cosine':
betas = cosine_beta_schedule(timesteps)
else:
raise ValueError(f'unknown beta schedule {beta_schedule}')
alphas = 1. - betas
alphas_cumprod = torch.cumprod(alphas, axis=0)
alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value=1.)
# Calculations for diffusion q(x_t | x_{t-1}) and others
self.register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
self.register_buffer('sqrt_recip_alphas_cumprod',
torch.sqrt(1. / alphas_cumprod))
self.register_buffer('sqrt_recipm1_alphas_cumprod',
torch.sqrt(1. / alphas_cumprod - 1))
self.register_buffer('sqrt_one_minus_alphas_cumprod',
torch.sqrt(1. - alphas_cumprod))
# Calculations for posterior q(x_{t-1} | x_t, x_0)
posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
self.register_buffer('posterior_variance', posterior_variance)
self.register_buffer(
'posterior_log_variance_clipped',
torch.log(posterior_variance.clamp(min=1e-20))
)
self.register_buffer(
'posterior_mean_coef1',
betas * torch.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod)
)
self.register_buffer(
'posterior_mean_coef2',
(1. - alphas_cumprod_prev) * torch.sqrt(alphas) / (1. - alphas_cumprod)
)
# p2 reweighting
p2_loss_weight = ((p2_loss_weight_k + alphas_cumprod / (1 - alphas_cumprod))
** (-p2_loss_weight_gamma))
self.register_buffer('p2_loss_weight', p2_loss_weight)
def default(self, val, d):
return vars(self.config)[val] if val in self.config else d
def train_step(self, x_0: Tensor, cond: Optional[Tensor] = None, t:Optional[Tensor] = None) -> Tensor:
N, device = x_0.shape[0], x_0.device
# If t is not none, use it, otherwise sample from uniform
if t is not None:
t = t.long().to(device)
else:
t = torch.randint(0, self.timesteps, (N,), device=device).long() # (N)
model_out, noise = self(x_0, t, cond=cond)
if self.objective == 'pred_noise':
target = noise # (N, C, H, W)
elif self.objective == 'pred_x_0':
target = x_0 # (N, C, H, W)
else:
raise ValueError(f'unknown objective {self.objective}')
loss = F.l1_loss(model_out, target, reduction='none') # (N, C, H, W)
loss = reduce(loss, 'b ... -> b (...)', 'mean') # (N, (C x H x W))
# p2 reweighting
loss = loss * get_index_from_list(self.p2_loss_weight, t, loss.shape)
return loss.mean()
def val_step(self, x_0: Tensor, cond: Optional[Tensor] = None, t_steps:Optional[int] = None) -> Tensor:
if not t_steps:
t_steps = self.timesteps
step_size = self.timesteps // t_steps
N, device = x_0.shape[0], x_0.device
losses = []
for t in range(0, self.timesteps, step_size):
t = torch.ones((N,)) * t
t = t.long().to(device)
losses.append(self.train_step(x_0, cond, t))
return torch.stack(losses).mean()
def forward(self, x_0: Tensor, t: Tensor, cond: Optional[Tensor] = None) -> Tensor:
"""
Noise x_0 for t timestep and get the model prediction.
:param x_0: Clean image, (N, C, H, W)
:param t: Timestep, (N,)
:param cond: element to condition the reconstruction on - eg image when x_0 is a segmentation (N, C', H, W)
:return pred: Model output, predicted noise or image, (N, C, H, W)
:return noise: Added noise, (N, C, H, W)
"""
if self.config.normalize:
x_0 = normalize_to_neg_one_to_one(x_0)
if cond is not None and self.config.normalize:
cond = normalize_to_neg_one_to_one(cond)
x_t, noise = self.forward_diffusion_model(x_0, t)
return self.model(x_t, t, cond), noise
def forward_diffusion_model(
self,
x_0: Tensor,
t: Tensor,
noise: Optional[Tensor] = None,
) -> Tuple[Tensor, Tensor]:
"""
Takes an image and a timestep as input and returns the noisy version
of it.
:param x_0: Image at timestep 0, (N, C, H, W)
:param t: Timestep, (N)
:param cond: element to condition the reconstruction on - eg image when x_0 is a segmentation (N, C', H, W)
:return x_t: Noisy image at timestep t, (N, C, H, W)
:return noise: Noise added to the image, (N, C, H, W)
"""
noise = default(noise, lambda: torch.randn_like(x_0))
sqrt_alphas_cumprod_t = get_index_from_list(
self.sqrt_alphas_cumprod, t, x_0.shape)
sqrt_one_minus_alphas_cumprod_t = get_index_from_list(
self.sqrt_one_minus_alphas_cumprod, t, x_0.shape)
# mean + variance
x_t = sqrt_alphas_cumprod_t * x_0 + sqrt_one_minus_alphas_cumprod_t * noise
return x_t, noise
@torch.no_grad()
def sample_timestep(self, x_t: Tensor, t: int, cond=Optional[Tensor]) -> Tensor:
"""
Sample from the model.
:param x_t: Image noised t times, (N, C, H, W)
:param t: Timestep
:return: Sampled image, (N, C, H, W)
"""
N = x_t.shape[0]
device = x_t.device
batched_t = torch.full((N,), t, device=device, dtype=torch.long) # (N)
model_mean, model_log_variance, _ = self.p_mean_variance(x_t, batched_t, cond=cond)
noise = torch.randn_like(x_t) if t > 0 else 0.
pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
return pred_img
def p_mean_variance(self, x_t: Tensor, t: Tensor, clip_denoised: bool = True, cond:Optional[Tensor] = None) -> Tuple[Tensor, Tensor, Tensor]:
_, pred_x_0 = self.model_predictions(x_t, t, cond=cond)
if clip_denoised:
# pred_x_0.clamp_(-1., 1.)
# Dynamic thrsholding
s = torch.quantile(rearrange(pred_x_0, 'b ... -> b (...)').abs(),
self.dynamic_threshold_percentile,
dim=1)
s = torch.max(s, torch.tensor(1.0))[:, None, None, None]
pred_x_0 = torch.clip(pred_x_0, -s, s) / s
(model_mean,
posterior_log_variance) = self.q_posterior(pred_x_0, x_t, t)
return model_mean, posterior_log_variance, pred_x_0
def model_predictions(self, x_t: Tensor, t: Tensor, cond:Optional[Tensor] = None) \
-> Tuple[Tensor, Tensor]:
"""
Return the predicted noise and x_0 for a given x_t and t.
:param x_t: Noised image at timestep t, (N, C, H, W)
:param t: Timestep, (N,)
:return pred_noise: Predicted noise, (N, C, H, W)
:return pred_x_0: Predicted x_0, (N, C, H, W)
"""
model_output = self.model(x_t, t, cond)
if self.objective == 'pred_noise':
pred_noise = model_output
pred_x_0 = self.predict_x_0_from_noise(x_t, t, model_output)
elif self.objective == 'pred_x_start':
pred_noise = self.predict_noise_from_x_0(x_t, t, model_output)
pred_x_0 = model_output
return pred_noise, pred_x_0
def q_posterior(self, x_start: Tensor, x_t: Tensor, t: Tensor) \
-> Tuple[Tensor, Tensor]:
posterior_mean = (
get_index_from_list(self.posterior_mean_coef1, t, x_t.shape) * x_start
+ get_index_from_list(self.posterior_mean_coef2, t, x_t.shape) * x_t
)
posterior_log_variance_clipped = get_index_from_list(
self.posterior_log_variance_clipped, t, x_t.shape)
return posterior_mean, posterior_log_variance_clipped
def predict_x_0_from_noise(self, x_t: Tensor, t: Tensor, noise: Tensor) \
-> Tensor:
"""
Get x_0 given x_t, t, and the known or predicted noise.
:param x_t: Noised image at timestep t, (N, C, H, W)
:param t: Timestep, (N,)
:param noise: Noise, (N, C, H, W)
:return: Predicted x_0, (N, C, H, W)
"""
return (
get_index_from_list(
self.sqrt_recip_alphas_cumprod, t, x_t.shape)
* x_t
- get_index_from_list(
self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
* noise
)
def predict_noise_from_x_0(self, x_t: Tensor, t: Tensor, x_0: Tensor) \
-> Tensor:
"""
Get noise given the known or predicted x_0, x_t, and t
:param x_t: Noised image at timestep t, (N, C, H, W)
:param t: Timestep, (N,)
:param noise: Noise, (N, C, H, W)
:return: Predicted noise, (N, C, H, W)
"""
return (
(get_index_from_list(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x_0)
/ get_index_from_list(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
)
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