improve ddim comments

models/vision/ddpm/modeling_ddpm.py

@@ -30,43 +30,43 @@ class DDPM(DiffusionPipeline):
             torch_device = "cuda" if torch.cuda.is_available() else "cpu"
 
         self.unet.to(torch_device)
-        # 1. Sample gaussian noise
+
+        # Sample gaussian noise to begin loop
         image = self.noise_scheduler.sample_noise(
             (batch_size, self.unet.in_channels, self.unet.resolution, self.unet.resolution),
             device=torch_device,
             generator=generator,
         )
-        for t in tqdm.tqdm(reversed(range(len(self.noise_scheduler))), total=len(self.noise_scheduler)):
-            # i) define coefficients for time step t
-            clipped_image_coeff = 1 / torch.sqrt(self.noise_scheduler.get_alpha_prod(t))
-            clipped_noise_coeff = torch.sqrt(1 / self.noise_scheduler.get_alpha_prod(t) - 1)
-            image_coeff = (
-                (1 - self.noise_scheduler.get_alpha_prod(t - 1))
-                * torch.sqrt(self.noise_scheduler.get_alpha(t))
-                / (1 - self.noise_scheduler.get_alpha_prod(t))
-            )
-            clipped_coeff = (
-                torch.sqrt(self.noise_scheduler.get_alpha_prod(t - 1))
-                * self.noise_scheduler.get_beta(t)
-                / (1 - self.noise_scheduler.get_alpha_prod(t))
-            )
 
-            # ii) predict noise residual
+        for t in tqdm.tqdm(reversed(range(len(self.noise_scheduler))), total=len(self.noise_scheduler)):
+            # 1. predict noise residual
             with torch.no_grad():
                 noise_residual = self.unet(image, t)
 
-            # iii) compute predicted image from residual
+            # 2. compute alphas, betas
+            alpha_prod_t = self.noise_scheduler.get_alpha_prod(t)
+            alpha_prod_t_prev = self.noise_scheduler.get_alpha_prod(t - 1)
+            beta_prod_t = 1 - alpha_prod_t
+            beta_prod_t_prev = 1 - alpha_prod_t_prev
+
+            # 3. compute predicted image from residual
             # See 2nd formula at https://github.com/hojonathanho/diffusion/issues/5#issue-896554416 for comparison
-            pred_mean = clipped_image_coeff * image - clipped_noise_coeff * noise_residual
+            # First: Compute inner formula
+            pred_mean = (1 / alpha_prod_t.sqrt()) * (image - beta_prod_t.sqrt() * noise_residual)
+            # Second: Clip
             pred_mean = torch.clamp(pred_mean, -1, 1)
-            prev_image = clipped_coeff * pred_mean + image_coeff * image
+            # Third: Compute outer coefficients
+            pred_mean_coeff = (alpha_prod_t_prev.sqrt() * self.noise_scheduler.get_beta(t)) / beta_prod_t
+            image_coeff = (beta_prod_t_prev * self.noise_scheduler.get_alpha(t).sqrt()) / beta_prod_t 
+            # Fourth: Compute outer formula
+            prev_image = pred_mean_coeff * pred_mean + image_coeff * image
 
-            # iv) sample variance
+            # 4. sample variance
             prev_variance = self.noise_scheduler.sample_variance(
                 t, prev_image.shape, device=torch_device, generator=generator
             )
 
-            # v) sample  x_{t-1} ~ N(prev_image, prev_variance)
+            # 5. sample  x_{t-1} ~ N(prev_image, prev_variance) = add variance to predicted image
             sampled_prev_image = prev_image + prev_variance
             image = sampled_prev_image