EulerDiscreteScheduler add rescale_betas_zero_snr (huggingface#6024)

* EulerDiscreteScheduler add `rescale_betas_zero_snr`

schedulers/scheduling_euler_discrete.py

@@ -92,6 +92,43 @@ def alpha_bar_fn(t):
     return torch.tensor(betas, dtype=torch.float32)
 
 
+# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
+def rescale_zero_terminal_snr(betas):
+    """
+    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
+
+
+    Args:
+        betas (`torch.FloatTensor`):
+            the betas that the scheduler is being initialized with.
+
+    Returns:
+        `torch.FloatTensor`: rescaled betas with zero terminal SNR
+    """
+    # Convert betas to alphas_bar_sqrt
+    alphas = 1.0 - betas
+    alphas_cumprod = torch.cumprod(alphas, dim=0)
+    alphas_bar_sqrt = alphas_cumprod.sqrt()
+
+    # Store old values.
+    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
+    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
+
+    # Shift so the last timestep is zero.
+    alphas_bar_sqrt -= alphas_bar_sqrt_T
+
+    # Scale so the first timestep is back to the old value.
+    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
+
+    # Convert alphas_bar_sqrt to betas
+    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
+    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
+    alphas = torch.cat([alphas_bar[0:1], alphas])
+    betas = 1 - alphas
+
+    return betas
+
+
 class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
     """
     Euler scheduler.
@@ -128,6 +165,10 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
             An offset added to the inference steps. You can use a combination of `offset=1` and
             `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
             Diffusion.
+        rescale_betas_zero_snr (`bool`, defaults to `False`):
+            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
+            dark samples instead of limiting it to samples with medium brightness. Loosely related to
+            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -149,6 +190,7 @@ def __init__(
         timestep_spacing: str = "linspace",
         timestep_type: str = "discrete",  # can be "discrete" or "continuous"
         steps_offset: int = 0,
+        rescale_betas_zero_snr: bool = False,
     ):
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
@@ -163,9 +205,17 @@ def __init__(
         else:
             raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
 
+        if rescale_betas_zero_snr:
+            self.betas = rescale_zero_terminal_snr(self.betas)
+
         self.alphas = 1.0 - self.betas
         self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
 
+        if rescale_betas_zero_snr:
+            # Close to 0 without being 0 so first sigma is not inf
+            # FP16 smallest positive subnormal works well here
+            self.alphas_cumprod[-1] = 2**-24
+
         sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
         timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
 
@@ -420,6 +470,9 @@ def step(
         if self.step_index is None:
             self._init_step_index(timestep)
 
+        # Upcast to avoid precision issues when computing prev_sample
+        sample = sample.to(torch.float32)
+
         sigma = self.sigmas[self.step_index]
 
         gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0
@@ -456,6 +509,9 @@ def step(
 
         prev_sample = sample + derivative * dt
 
+        # Cast sample back to model compatible dtype
+        prev_sample = prev_sample.to(model_output.dtype)
+
         # upon completion increase step index by one
         self._step_index += 1