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import torch.nn as nn
import numpy as np
from typing import Optional, Tuple, Union
import math
class BetaScheduler:
"""Beta调度器"""
@staticmethod
def linear(num_timesteps: int, beta_start: float = 0.0001, beta_end: float = 0.02) -> np.ndarray:
"""线性调度"""
return np.linspace(beta_start, beta_end, num_timesteps, dtype=np.float32)
@staticmethod
def cosine(num_timesteps: int, s: float = 0.008) -> np.ndarray:
"""余弦调度"""
steps = num_timesteps + 1
x = np.linspace(0, num_timesteps, steps)
alphas_cumprod = np.cos(((x / num_timesteps) + s) / (1 + s) * np.pi * 0.5) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
return np.clip(betas, 0, 0.999)
@staticmethod
def scaled_linear(num_timesteps: int) -> np.ndarray:
"""缩放线性调度(Stable Diffusion默认)"""
beta_start = 0.00085
beta_end = 0.012
return np.linspace(beta_start**0.5, beta_end**0.5, num_timesteps) ** 2
class DiffusionProcess:
"""扩散过程管理"""
def __init__(self, config: dict):
self.config = config
diff_config = config.get('diffusion', {})
self.num_train_timesteps = diff_config.get('num_train_timesteps', 1000)
self.num_inference_timesteps = diff_config.get('num_inference_timesteps', 50)
self.beta_start = diff_config.get('beta_start', 0.00085)
self.beta_end = diff_config.get('beta_end', 0.012)
self.beta_schedule = diff_config.get('beta_schedule', 'scaled_linear')
self.prediction_type = diff_config.get('prediction_type', 'epsilon')
# 初始化调度参数
self._init_schedule()
def _init_schedule(self):
"""初始化扩散调度参数"""
# 计算betas
if self.beta_schedule == "linear":
betas = BetaScheduler.linear(
self.num_train_timesteps,
self.beta_start,
self.beta_end
)
elif self.beta_schedule == "cosine":
betas = BetaScheduler.cosine(self.num_train_timesteps)
elif self.beta_schedule == "scaled_linear":
betas = BetaScheduler.scaled_linear(self.num_train_timesteps)
else:
raise ValueError(f"Unknown beta schedule: {self.beta_schedule}")
self.betas = torch.from_numpy(betas).float()
# 计算alphas
self.alphas = 1.0 - self.betas
self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
self.alphas_cumprod_prev = F.pad(self.alphas_cumprod[:-1], (1, 0), value=1.0)
# 计算扩散后验方差
self.variance = self.betas * (1.0 - self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod)
# 注册为buffer
self.register_buffer = lambda name, tensor: setattr(self, name, tensor)
self.register_buffer('betas', self.betas)
self.register_buffer('alphas', self.alphas)
self.register_buffer('alphas_cumprod', self.alphas_cumprod)
self.register_buffer('alphas_cumprod_prev', self.alphas_cumprod_prev)
self.register_buffer('variance', self.variance)
# 计算采样系数
self.register_buffer('sqrt_alphas_cumprod', torch.sqrt(self.alphas_cumprod))
self.register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1.0 - self.alphas_cumprod))
self.register_buffer('log_one_minus_alphas_cumprod', torch.log(1.0 - self.alphas_cumprod))
self.register_buffer('sqrt_recip_alphas_cumprod', torch.sqrt(1.0 / self.alphas_cumprod))
self.register_buffer('sqrt_recipm1_alphas_cumprod', torch.sqrt(1.0 / self.alphas_cumprod - 1))
def q_sample(self, x_start: torch.Tensor, t: torch.Tensor, noise: Optional[torch.Tensor] = None) -> torch.Tensor:
"""前向扩散过程:加噪"""
if noise is None:
noise = torch.randn_like(x_start)
sqrt_alphas_cumprod_t = self.extract(self.sqrt_alphas_cumprod, t, x_start.shape)
sqrt_one_minus_alphas_cumprod_t = self.extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape)
return sqrt_alphas_cumprod_t * x_start + sqrt_one_minus_alphas_cumprod_t * noise
def extract(self, a: torch.Tensor, t: torch.Tensor, x_shape: Tuple[int, ...]) -> torch.Tensor:
"""从张量a中提取索引t处的值"""
batch_size = t.shape[0]
out = a.gather(-1, t.cpu())
return out.reshape(batch_size, *((1,) * (len(x_shape) - 1))).to(t.device)
def get_loss_weight(self, snr: torch.Tensor, gamma: float = 5.0) -> torch.Tensor:
"""根据SNR计算损失权重"""
if gamma is None:
return torch.ones_like(snr)
snr = torch.clamp(snr, min=1e-8)
min_snr = torch.tensor(gamma, device=snr.device)
weight = torch.minimum(snr, min_snr) / snr
return weight
def compute_snr(self, timesteps: torch.Tensor) -> torch.Tensor:
"""计算信噪比(SNR)"""
alphas_cumprod = self.extract(self.alphas_cumprod, timesteps, timesteps.shape)
snr = alphas_cumprod / (1 - alphas_cumprod)
return snr
class DDIMScheduler:
"""DDIM采样器"""
def __init__(self, diffusion: DiffusionProcess):
self.diffusion = diffusion
self.num_train_timesteps = diffusion.num_train_timesteps
self.num_inference_timesteps = diffusion.num_inference_timesteps
# 设置时间步
self.set_timesteps(self.num_inference_timesteps)
def set_timesteps(self, num_inference_timesteps: int):
"""设置推理时间步"""
self.num_inference_timesteps = num_inference_timesteps
# 选择时间步
if self.num_train_timesteps == self.num_inference_timesteps:
self.timesteps = torch.arange(0, self.num_train_timesteps).long()
else:
step_ratio = self.num_train_timesteps // self.num_inference_timesteps
self.timesteps = torch.arange(0, self.num_train_timesteps, step_ratio).long()
self.timesteps = self.timesteps.flip(0) # 从T到0
@torch.no_grad()
def step(self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, eta: float = 0.0) -> torch.Tensor:
"""DDIM单步采样"""
# 获取当前时间步的参数
prev_timestep = timestep - self.num_train_timesteps // self.num_inference_timesteps
# 提取alpha参数
alpha_prod_t = self.diffusion.extract(self.diffusion.alphas_cumprod, timestep, sample.shape)
alpha_prod_t_prev = self.diffusion.extract(
self.diffusion.alphas_cumprod,
prev_timestep,
sample.shape
) if prev_timestep >= 0 else torch.ones_like(alpha_prod_t)
# 根据预测类型处理模型输出
if self.diffusion.prediction_type == "epsilon":
pred_original_sample = (sample - (1 - alpha_prod_t) ** 0.5 * model_output) / alpha_prod_t ** 0.5
pred_epsilon = model_output
elif self.diffusion.prediction_type == "sample":
pred_original_sample = model_output
pred_epsilon = (sample - alpha_prod_t ** 0.5 * pred_original_sample) / (1 - alpha_prod_t) ** 0.5
elif self.diffusion.prediction_type == "v_prediction":
pred_original_sample = (alpha_prod_t ** 0.5) * sample - (1 - alpha_prod_t) ** 0.5 * model_output
pred_epsilon = (alpha_prod_t ** 0.5) * model_output + (1 - alpha_prod_t) ** 0.5 * sample
else:
raise ValueError(f"Unsupported prediction type: {self.diffusion.prediction_type}")
# 计算x_t-1的方差
variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
std_dev_t = eta * variance ** 0.5
# 计算x_t-1的均值
pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon
prev_sample = alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction
# 添加噪声
if eta > 0:
noise = torch.randn_like(model_output)
prev_sample = prev_sample + std_dev_t * noise
return prev_sample
class DiffusionModel(nn.Module):
"""扩散模型封装"""
def __init__(self, unet: nn.Module, diffusion: DiffusionProcess):
super().__init__()
self.unet = unet
self.diffusion = diffusion
self.scheduler = DDIMScheduler(diffusion)
def forward(self, x: torch.Tensor, timesteps: torch.Tensor, context: torch.Tensor) -> torch.Tensor:
"""前向传播:预测噪声"""
return self.unet(x, timesteps, context)
def compute_loss(self, x_start: torch.Tensor, context: torch.Tensor, noise: Optional[torch.Tensor] = None) -> torch.Tensor:
"""计算扩散损失"""
if noise is None:
noise = torch.randn_like(x_start)
# 随机采样时间步
batch_size = x_start.shape[0]
timesteps = torch.randint(
0, self.diffusion.num_train_timesteps,
(batch_size,), device=x_start.device
).long()
# 前向扩散
x_noisy = self.diffusion.q_sample(x_start, timesteps, noise)
# 预测噪声
predicted_noise = self.unet(x_noisy, timesteps, context)
# 计算损失
loss = F.mse_loss(predicted_noise, noise)
return loss
@torch.no_grad()
def generate(
self,
context: torch.Tensor,
num_samples: int = 1,
height: int = 512,
width: int = 512,
guidance_scale: float = 7.5
) -> torch.Tensor:
"""生成图像"""
# 初始化噪声
latents = torch.randn(
(num_samples, self.unet.in_channels, height // 8, width // 8),
device=next(self.unet.parameters()).device
)
# DDIM采样
self.scheduler.set_timesteps(self.diffusion.num_inference_timesteps)
for t in self.scheduler.timesteps:
# 扩展latents以匹配批大小
latent_model_input = torch.cat([latents] * 2) if guidance_scale > 1.0 else latents
latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
# 预测噪声
timesteps = torch.full((num_samples,), t, device=latents.device).long()
if guidance_scale > 1.0:
timesteps = torch.cat([timesteps] * 2)
noise_pred = self.unet(latent_model_input, timesteps, context)
# 应用分类器自由引导
if guidance_scale > 1.0:
noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
# 计算上一个样本
latents = self.scheduler.step(noise_pred, t, latents).prev_sample
return latents |