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import numpy as np
from typing import Tuple, Optional
class NoiseScheduler:
"""Diffusion noise scheduler with cosine schedule."""
def __init__(self, num_timesteps: int = 1000, schedule_type: str = "cosine"):
self.num_timesteps = num_timesteps
self.schedule_type = schedule_type
if schedule_type == "cosine":
# Cosine schedule (more stable for small images)
s = 0.008
steps = num_timesteps + 1
x = torch.linspace(0, num_timesteps, steps)
alpha_bars = torch.cos(((x / num_timesteps) + s) / (1 + s) * torch.pi * 0.5) ** 2
alpha_bars = alpha_bars / alpha_bars[0] # Normalize
alphas = alpha_bars[1:] / alpha_bars[:-1]
alphas = torch.clamp(alphas, 0.0001, 0.9999)
else:
# Linear schedule (original DDPM)
betas = torch.linspace(1e-4, 0.02, num_timesteps)
alphas = 1.0 - betas
alphas_cumprod = torch.cumprod(alphas, dim=0)
# Pre-compute values for training
self.register_buffer('alphas', alphas)
self.register_buffer('alphas_cumprod', alphas_cumprod)
self.register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
self.register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1.0 - alphas_cumprod))
def register_buffer(self, name: str, tensor: torch.Tensor):
"""Register a buffer that persists with the module."""
setattr(self, name, tensor)
def sample_timesteps(self, batch_size: int, device: torch.device) -> torch.Tensor:
"""Sample random timesteps for training."""
return torch.randint(0, self.num_timesteps, (batch_size,), device=device, dtype=torch.long)
def add_noise(self, x_0: torch.Tensor, t: torch.Tensor, noise: Optional[torch.Tensor] = None) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Add noise to clean images according to diffusion forward process.
Args:
x_0: Clean images [B, C, H, W]
t: Timestep indices [B]
noise: Optional pre-sampled noise
Returns:
x_t: Noisy images
noise: The noise that was added
"""
if noise is None:
noise = torch.randn_like(x_0)
# Ensure buffers are on the same device as input
if self.sqrt_alphas_cumprod.device != x_0.device:
self.sqrt_alphas_cumprod = self.sqrt_alphas_cumprod.to(x_0.device)
self.sqrt_one_minus_alphas_cumprod = self.sqrt_one_minus_alphas_cumprod.to(x_0.device)
# Get sqrt(alpha_bar) and sqrt(1-alpha_bar) for each timestep
sqrt_alpha_bar = self.sqrt_alphas_cumprod[t].view(-1, 1, 1, 1)
sqrt_one_minus_alpha_bar = self.sqrt_one_minus_alphas_cumprod[t].view(-1, 1, 1, 1)
# Forward diffusion: x_t = sqrt(alpha_bar) * x_0 + sqrt(1-alpha_bar) * epsilon
x_t = sqrt_alpha_bar * x_0 + sqrt_one_minus_alpha_bar * noise
return x_t, noise
def get_sampling_schedule(self, num_samples: int = None) -> np.ndarray:
"""Get timesteps for sampling (reverse process)."""
if num_samples is None:
return np.arange(self.num_timesteps - 1, -1, -1)
else:
return np.linspace(self.num_timesteps - 1, 0, num_samples, dtype=int)
@torch.no_grad()
def sample_diffusion(
model: torch.nn.Module,
scheduler: NoiseScheduler,
shape: Tuple[int, int, int],
device: torch.device,
num_steps: Optional[int] = None,
guidance_scale: float = 1.0,
clip_x0: bool = True
) -> torch.Tensor:
"""
Generate samples using the reverse diffusion process.
Args:
model: Trained U-Net model
scheduler: Noise scheduler
shape: (C, H, W) output shape
device: Device to run on
num_steps: Number of denoising steps (None = use all)
guidance_scale: Classifier-free guidance scale (1.0 = no guidance)
clip_x0: Whether to clip predicted x_0 to [-1, 1]
Returns:
Generated images in range [-1, 1]
"""
model.eval()
batch_size = shape[0] if len(shape) == 4 else 1
c, h, w = shape[-3:]
# Start from pure noise
x = torch.randn(batch_size, c, h, w, device=device)
# Get timesteps
if num_steps is None:
timesteps = scheduler.get_sampling_schedule()
else:
timesteps = scheduler.get_sampling_schedule(num_steps)
# Sampling loop
for i, t in enumerate(timesteps):
t_batch = torch.full((batch_size,), t, device=device, dtype=torch.long)
# Predict noise
noise_pred = model(x, t_batch)
# Compute alpha values for this timestep
alpha_bar = scheduler.alphas_cumprod[t]
alpha = scheduler.alphas[t] if t > 0 else torch.tensor(1.0, device=device)
# Posterior variance
if t == 0:
variance = 0
else:
beta = 1 - alpha
variance = beta * (1 - alpha_bar) / (1 - alpha)
# Denoise step (simplified DDIM-style for speed)
if guidance_scale != 1.0:
# Classifier-free guidance would go here (requires conditional model)
pass
# Compute predicted x_0
pred_x0 = (x - noise_pred * torch.sqrt(1 - alpha_bar)) / torch.sqrt(alpha_bar)
if clip_x0:
pred_x0 = torch.clamp(pred_x0, -1, 1)
# Compute direction to next timestep
if t == 0:
x = pred_x0
else:
prev_alpha_bar = scheduler.alphas_cumprod[t - 1]
direction = torch.sqrt(1 - prev_alpha_bar) * noise_pred
x = torch.sqrt(prev_alpha_bar) * pred_x0 + direction
# Add variance (optional, can be deterministic)
if variance > 0:
if isinstance(variance, torch.Tensor):
var_tensor = variance.clone().detach().to(device=device, dtype=torch.float32)
else:
var_tensor = torch.tensor(variance, device=device, dtype=torch.float32)
x += torch.randn_like(x) * torch.sqrt(var_tensor)
return torch.clamp(x, -1, 1)
def interpolate_images(
model: torch.nn.Module,
scheduler: NoiseScheduler,
img1: torch.Tensor,
img2: torch.Tensor,
num_interpolations: int = 5,
device: Optional[torch.device] = None
) -> torch.Tensor:
"""
Interpolate between two latent representations and generate images.
Args:
model: Trained U-Net model
scheduler: Noise scheduler
img1: First image [1, C, H, W]
img2: Second image [1, C, H, W]
num_interpolations: Number of intermediate images
device: Device to run on
Returns:
Interpolated images [num_interpolations+2, C, H, W]
"""
if device is None:
device = next(model.parameters()).device
img1 = img1.to(device)
img2 = img2.to(device)
# Add same noise to both images at high timestep
t_high = torch.tensor([scheduler.num_timesteps - 1], device=device)
noise = torch.randn_like(img1)
x1_noisy, _ = scheduler.add_noise(img1, t_high, noise)
x2_noisy, _ = scheduler.add_noise(img2, t_high, noise)
# Interpolate in noisy space
interpolated_noisy = []
for alpha in torch.linspace(0, 1, num_interpolations + 2):
interp = (1 - alpha) * x1_noisy + alpha * x2_noisy
interpolated_noisy.append(interp)
interpolated_noisy = torch.cat(interpolated_noisy, dim=0)
# Denoise all interpolated images
# Note: This is a simplified approach - proper interpolation requires more careful handling
results = []
for interp in interpolated_noisy:
x = interp.unsqueeze(0)
timesteps = scheduler.get_sampling_schedule()
for t in timesteps:
t_batch = torch.tensor([t], device=device)
noise_pred = model(x, t_batch)
alpha_bar = scheduler.alphas_cumprod[t]
alpha = scheduler.alphas[t] if t > 0 else torch.tensor(1.0, device=device)
pred_x0 = (x - noise_pred * torch.sqrt(1 - alpha_bar)) / torch.sqrt(alpha_bar)
pred_x0 = torch.clamp(pred_x0, -1, 1)
if t == 0:
x = pred_x0
else:
prev_alpha_bar = scheduler.alphas_cumprod[t - 1]
direction = torch.sqrt(1 - prev_alpha_bar) * noise_pred
x = torch.sqrt(prev_alpha_bar) * pred_x0 + direction
results.append(x)
return torch.cat(results, dim=0)
if __name__ == "__main__":
# Test the diffusion utilities
print("Testing NoiseScheduler...")
scheduler = NoiseScheduler(num_timesteps=1000)
# Test adding noise
x_clean = torch.randn(2, 3, 64, 64)
t = torch.randint(0, 1000, (2,))
x_noisy, noise = scheduler.add_noise(x_clean, t)
print(f"Clean image range: [{x_clean.min():.3f}, {x_clean.max():.3f}]")
print(f"Noisy image range: [{x_noisy.min():.3f}, {x_noisy.max():.3f}]")
print(f"Noise shape: {noise.shape}")
# Test that we can recover approximate original at t=0
t_zero = torch.zeros(2, dtype=torch.long)
x_almost_clean, _ = scheduler.add_noise(x_clean, t_zero)
mse = torch.mean((x_almost_clean - x_clean) ** 2)
print(f"MSE at t=0 (should be ~0): {mse:.6f}")
print("\nNoiseScheduler tests passed!")
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