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from abc import abstractmethod, ABC
import torch
class SchedulerInterface(ABC):
"""
Base class for diffusion noise schedule.
"""
alphas_cumprod: torch.Tensor # [T], alphas for defining the noise schedule
@abstractmethod
def add_noise(
self, clean_latent: torch.Tensor,
noise: torch.Tensor, timestep: torch.Tensor
):
"""
Diffusion forward corruption process.
Input:
- clean_latent: the clean latent with shape [B, C, H, W]
- noise: the noise with shape [B, C, H, W]
- timestep: the timestep with shape [B]
Output: the corrupted latent with shape [B, C, H, W]
"""
pass
def convert_x0_to_noise(
self, x0: torch.Tensor, xt: torch.Tensor,
timestep: torch.Tensor
) -> torch.Tensor:
"""
Convert the diffusion network's x0 prediction to noise predidction.
x0: the predicted clean data with shape [B, C, H, W]
xt: the input noisy data with shape [B, C, H, W]
timestep: the timestep with shape [B]
noise = (xt-sqrt(alpha_t)*x0) / sqrt(beta_t) (eq 11 in https://arxiv.org/abs/2311.18828)
"""
# use higher precision for calculations
original_dtype = x0.dtype
x0, xt, alphas_cumprod = map(
lambda x: x.double().to(x0.device), [x0, xt,
self.alphas_cumprod]
)
alpha_prod_t = alphas_cumprod[timestep].reshape(-1, 1, 1, 1)
beta_prod_t = 1 - alpha_prod_t
noise_pred = (xt - alpha_prod_t **
(0.5) * x0) / beta_prod_t ** (0.5)
return noise_pred.to(original_dtype)
def convert_noise_to_x0(
self, noise: torch.Tensor, xt: torch.Tensor,
timestep: torch.Tensor
) -> torch.Tensor:
"""
Convert the diffusion network's noise prediction to x0 predidction.
noise: the predicted noise with shape [B, C, H, W]
xt: the input noisy data with shape [B, C, H, W]
timestep: the timestep with shape [B]
x0 = (x_t - sqrt(beta_t) * noise) / sqrt(alpha_t) (eq 11 in https://arxiv.org/abs/2311.18828)
"""
# use higher precision for calculations
original_dtype = noise.dtype
noise, xt, alphas_cumprod = map(
lambda x: x.double().to(noise.device), [noise, xt,
self.alphas_cumprod]
)
alpha_prod_t = alphas_cumprod[timestep].reshape(-1, 1, 1, 1)
beta_prod_t = 1 - alpha_prod_t
x0_pred = (xt - beta_prod_t **
(0.5) * noise) / alpha_prod_t ** (0.5)
return x0_pred.to(original_dtype)
def convert_velocity_to_x0(
self, velocity: torch.Tensor, xt: torch.Tensor,
timestep: torch.Tensor
) -> torch.Tensor:
"""
Convert the diffusion network's velocity prediction to x0 predidction.
velocity: the predicted noise with shape [B, C, H, W]
xt: the input noisy data with shape [B, C, H, W]
timestep: the timestep with shape [B]
v = sqrt(alpha_t) * noise - sqrt(beta_t) x0
noise = (xt-sqrt(alpha_t)*x0) / sqrt(beta_t)
given v, x_t, we have
x0 = sqrt(alpha_t) * x_t - sqrt(beta_t) * v
see derivations https://chatgpt.com/share/679fb6c8-3a30-8008-9b0e-d1ae892dac56
"""
# use higher precision for calculations
original_dtype = velocity.dtype
velocity, xt, alphas_cumprod = map(
lambda x: x.double().to(velocity.device), [velocity, xt,
self.alphas_cumprod]
)
alpha_prod_t = alphas_cumprod[timestep].reshape(-1, 1, 1, 1)
beta_prod_t = 1 - alpha_prod_t
x0_pred = (alpha_prod_t ** 0.5) * xt - (beta_prod_t ** 0.5) * velocity
return x0_pred.to(original_dtype)
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