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import math
from dataclasses import dataclass
import torch
@dataclass
class NoiseSchedule:
"""
Precomputed DDPM noise schedule.
Main variables:
beta_t:
amount of noise added at timestep t
alpha_t:
1 - beta_t
alpha_bar_t:
cumulative product of alphas up to t
q(z_t | z_0):
z_t = sqrt(alpha_bar_t) * z_0
+ sqrt(1 - alpha_bar_t) * eps
"""
betas: torch.Tensor
alphas: torch.Tensor
alphas_cumprod: torch.Tensor
alphas_cumprod_prev: torch.Tensor
sqrt_alphas_cumprod: torch.Tensor
sqrt_one_minus_alphas_cumprod: torch.Tensor
log_one_minus_alphas_cumprod: torch.Tensor
sqrt_recip_alphas_cumprod: torch.Tensor
sqrt_recipm1_alphas_cumprod: torch.Tensor
posterior_variance: torch.Tensor
posterior_log_variance_clipped: torch.Tensor
posterior_mean_coef1: torch.Tensor
posterior_mean_coef2: torch.Tensor
num_timesteps: int
schedule_type: str
def to(self, device: torch.device | str) -> "NoiseSchedule":
device = torch.device(device)
return NoiseSchedule(
betas=self.betas.to(device),
alphas=self.alphas.to(device),
alphas_cumprod=self.alphas_cumprod.to(device),
alphas_cumprod_prev=self.alphas_cumprod_prev.to(device),
sqrt_alphas_cumprod=self.sqrt_alphas_cumprod.to(device),
sqrt_one_minus_alphas_cumprod=self.sqrt_one_minus_alphas_cumprod.to(device),
log_one_minus_alphas_cumprod=self.log_one_minus_alphas_cumprod.to(device),
sqrt_recip_alphas_cumprod=self.sqrt_recip_alphas_cumprod.to(device),
sqrt_recipm1_alphas_cumprod=self.sqrt_recipm1_alphas_cumprod.to(device),
posterior_variance=self.posterior_variance.to(device),
posterior_log_variance_clipped=self.posterior_log_variance_clipped.to(device),
posterior_mean_coef1=self.posterior_mean_coef1.to(device),
posterior_mean_coef2=self.posterior_mean_coef2.to(device),
num_timesteps=self.num_timesteps,
schedule_type=self.schedule_type,
)
def make_beta_schedule(
schedule_type: str = "cosine",
num_timesteps: int = 1000,
beta_start: float = 1e-4,
beta_end: float = 2e-2,
cosine_s: float = 0.008,
max_beta: float = 0.999,
) -> torch.Tensor:
"""
Create beta schedule.
Supported:
linear:
Standard DDPM linear beta schedule.
cosine:
Improved DDPM cosine schedule.
Usually better behaved and good default for v-prediction.
Returns:
betas: [num_timesteps], float32
"""
schedule_type = schedule_type.lower()
if schedule_type == "linear":
betas = torch.linspace(
beta_start,
beta_end,
num_timesteps,
dtype=torch.float64,
)
elif schedule_type == "cosine":
betas = cosine_beta_schedule(
num_timesteps=num_timesteps,
cosine_s=cosine_s,
max_beta=max_beta,
)
else:
raise ValueError(
f"Unknown schedule_type={schedule_type}. "
"Use 'linear' or 'cosine'."
)
return betas.float()
def cosine_beta_schedule(
num_timesteps: int,
cosine_s: float = 0.008,
max_beta: float = 0.999,
) -> torch.Tensor:
"""
Cosine beta schedule
Instead of directly defining beta_t, we define alpha_bar(t)
using a cosine curve, then derive beta_t.
"""
steps = num_timesteps + 1
x = torch.linspace(
0,
num_timesteps,
steps,
dtype=torch.float64,
)
alphas_cumprod = torch.cos(
((x / num_timesteps) + cosine_s)
/ (1.0 + cosine_s)
* math.pi
* 0.5
) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
betas = 1.0 - (
alphas_cumprod[1:] / alphas_cumprod[:-1]
)
betas = torch.clamp(
betas,
min=1e-8,
max=max_beta,
)
return betas
def create_noise_schedule(
schedule_type: str = "cosine",
num_timesteps: int = 1000,
beta_start: float = 1e-4,
beta_end: float = 2e-2,
cosine_s: float = 0.008,
max_beta: float = 0.999,
) -> NoiseSchedule:
"""
all precomputed schedule tensors needed for DDPM training and sampling.
"""
betas = make_beta_schedule(
schedule_type=schedule_type,
num_timesteps=num_timesteps,
beta_start=beta_start,
beta_end=beta_end,
cosine_s=cosine_s,
max_beta=max_beta,
)
alphas = 1.0 - betas
alphas_cumprod = torch.cumprod(
alphas,
dim=0,
)
alphas_cumprod_prev = torch.cat(
[
torch.ones(1, dtype=alphas_cumprod.dtype),
alphas_cumprod[:-1],
],
dim=0,
)
sqrt_alphas_cumprod = torch.sqrt(alphas_cumprod)
sqrt_one_minus_alphas_cumprod = torch.sqrt(
1.0 - alphas_cumprod
)
log_one_minus_alphas_cumprod = torch.log(
torch.clamp(
1.0 - alphas_cumprod,
min=1e-20,
)
)
sqrt_recip_alphas_cumprod = torch.sqrt(
1.0 / alphas_cumprod
)
sqrt_recipm1_alphas_cumprod = torch.sqrt(
1.0 / alphas_cumprod - 1.0
)
# Posterior q(z_{t-1} | z_t, z_0)
posterior_variance = (
betas
* (1.0 - alphas_cumprod_prev)
/ (1.0 - alphas_cumprod)
)
posterior_log_variance_clipped = torch.log(
torch.clamp(
posterior_variance,
min=1e-20,
)
)
posterior_mean_coef1 = (
betas
* torch.sqrt(alphas_cumprod_prev)
/ (1.0 - alphas_cumprod)
)
posterior_mean_coef2 = (
(1.0 - alphas_cumprod_prev)
* torch.sqrt(alphas)
/ (1.0 - alphas_cumprod)
)
return NoiseSchedule(
betas=betas,
alphas=alphas,
alphas_cumprod=alphas_cumprod,
alphas_cumprod_prev=alphas_cumprod_prev,
sqrt_alphas_cumprod=sqrt_alphas_cumprod,
sqrt_one_minus_alphas_cumprod=sqrt_one_minus_alphas_cumprod,
log_one_minus_alphas_cumprod=log_one_minus_alphas_cumprod,
sqrt_recip_alphas_cumprod=sqrt_recip_alphas_cumprod,
sqrt_recipm1_alphas_cumprod=sqrt_recipm1_alphas_cumprod,
posterior_variance=posterior_variance,
posterior_log_variance_clipped=posterior_log_variance_clipped,
posterior_mean_coef1=posterior_mean_coef1,
posterior_mean_coef2=posterior_mean_coef2,
num_timesteps=num_timesteps,
schedule_type=schedule_type,
)
def extract(
values: torch.Tensor,
timesteps: torch.Tensor,
broadcast_shape: tuple[int, ...],
) -> torch.Tensor:
"""
Extract values[t] and reshape for broadcasting.
Args:
values:
Schedule tensor with shape [T].
timesteps:
Long tensor with shape [B].
broadcast_shape:
Shape of target tensor, e.g. z_t.shape = [B, C, H, W].
Returns:
Tensor with shape [B, 1, 1, 1], broadcastable to broadcast_shape.
Example:
sqrt_alpha_bar_t = extract(
schedule.sqrt_alphas_cumprod,
t,
z_0.shape,
)
"""
if timesteps.dtype != torch.long:
timesteps = timesteps.long()
out = values.gather(
dim=0,
index=timesteps,
)
while len(out.shape) < len(broadcast_shape):
out = out[..., None]
return out |