UniPC Multistep add `rescale_betas_zero_snr` (#7531)

* UniPC Multistep add `rescale_betas_zero_snr`

Same patch as DPM and Euler with the patched final alpha cumprod

BF16 doesn't seem to break down, I think cause UniPC upcasts during some
phases already? We could still force an upcast since it only
loses ≈ 0.005 it/s for me but the difference in output is very small. A
better endeavor might upcasting in step() and removing all the other
upcasts elsewhere?

* UniPC ZSNR UT

* Re-add `rescale_betas_zsnr` doc oops

src/diffusers/schedulers/scheduling_unipc_multistep.py

@@ -71,6 +71,43 @@ def betas_for_alpha_bar(
     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 UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
     """
     `UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.
@@ -130,6 +167,10 @@ class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
         final_sigmas_type (`str`, defaults to `"zero"`):
             The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
             sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
+        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]
@@ -157,6 +198,7 @@ class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
         timestep_spacing: str = "linspace",
         steps_offset: int = 0,
         final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
+        rescale_betas_zero_snr: bool = False,
     ):
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
@@ -171,8 +213,17 @@ class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
         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
+
         # Currently we only support VP-type noise schedule
         self.alpha_t = torch.sqrt(self.alphas_cumprod)
         self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)

tests/schedulers/test_scheduler_unipc.py

@@ -180,6 +180,10 @@ class UniPCMultistepSchedulerTest(SchedulerCommonTest):
         for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=prediction_type)
 
+    def test_rescale_betas_zero_snr(self):
+        for rescale_betas_zero_snr in [True, False]:
+            self.check_over_configs(rescale_betas_zero_snr=rescale_betas_zero_snr)
+
     def test_solver_order_and_type(self):
         for solver_type in ["bh1", "bh2"]:
             for order in [1, 2, 3]: