Add Laplace scheduler that samples more around mid-range noise levels (around log SNR=0), increasing performance (lower FID) with faster convergence speed, and robust to resolution and objective. Reference: https://arxiv.org/pdf/2407.03297.

Author: gapatron

Diff for: src/diffusers/schedulers/scheduling_ddpm.py

@@ -72,6 +72,13 @@ def betas_for_alpha_bar(
 
         def alpha_bar_fn(t):
             return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
+        
+    elif alpha_transform_type == "laplace":
+
+        def alpha_bar_fn(t):
+            lmb = - 0.5 * math.copysign(1, 0.5 - t) * math.log(1 - 2 * math.fabs(0.5 - t) + 1e-6)
+            snr = math.exp(lmb)
+            return math.sqrt(snr / (1 + snr))
 
     elif alpha_transform_type == "exp":
 
@@ -206,6 +213,8 @@ def __init__(
         elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             self.betas = betas_for_alpha_bar(num_train_timesteps)
+        elif beta_schedule == "laplace":
+            self.betas = betas_for_alpha_bar(num_train_timesteps, alpha_transform_type="laplace")
         elif beta_schedule == "sigmoid":
             # GeoDiff sigmoid schedule
             betas = torch.linspace(-6, 6, num_train_timesteps)