Add `Karras sigmas` to HeunDiscreteScheduler (#3160)

* Add karras pattern to discrete heun scheduler

* Add integration test

* Fix failing CI on pytorch test on M1 (mps)

---------
Co-authored-by: Patrick von Platen <patrick.v.platen@gmail.com>

src/diffusers/schedulers/scheduling_heun_discrete.py

@@ -75,7 +75,11 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         prediction_type (`str`, default `epsilon`, optional):
             prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
             process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
-            https://imagen.research.google/video/paper.pdf)
+            https://imagen.research.google/video/paper.pdf).
+        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
+             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
+             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
+             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -90,6 +94,7 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         beta_schedule: str = "linear",
         trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
         prediction_type: str = "epsilon",
+        use_karras_sigmas: Optional[bool] = False,
     ):
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
@@ -111,6 +116,7 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
 
         #  set all values
         self.set_timesteps(num_train_timesteps, None, num_train_timesteps)
+        self.use_karras_sigmas = use_karras_sigmas
 
     def index_for_timestep(self, timestep, schedule_timesteps=None):
         if schedule_timesteps is None:
@@ -165,7 +171,13 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         timesteps = np.linspace(0, num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()
 
         sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        log_sigmas = np.log(sigmas)
         sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
+
+        if self.use_karras_sigmas:
+            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
+
         sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
         sigmas = torch.from_numpy(sigmas).to(device=device)
         self.sigmas = torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2), sigmas[-1:]])
@@ -186,6 +198,44 @@ class HeunDiscreteScheduler(SchedulerMixin, ConfigMixin):
         self.prev_derivative = None
         self.dt = None
 
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
+    def _sigma_to_t(self, sigma, log_sigmas):
+        # get log sigma
+        log_sigma = np.log(sigma)
+
+        # get distribution
+        dists = log_sigma - log_sigmas[:, np.newaxis]
+
+        # get sigmas range
+        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
+        high_idx = low_idx + 1
+
+        low = log_sigmas[low_idx]
+        high = log_sigmas[high_idx]
+
+        # interpolate sigmas
+        w = (low - log_sigma) / (low - high)
+        w = np.clip(w, 0, 1)
+
+        # transform interpolation to time range
+        t = (1 - w) * low_idx + w * high_idx
+        t = t.reshape(sigma.shape)
+        return t
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
+    def _convert_to_karras(self, in_sigmas: torch.FloatTensor, num_inference_steps) -> torch.FloatTensor:
+        """Constructs the noise schedule of Karras et al. (2022)."""
+
+        sigma_min: float = in_sigmas[-1].item()
+        sigma_max: float = in_sigmas[0].item()
+
+        rho = 7.0  # 7.0 is the value used in the paper
+        ramp = np.linspace(0, 1, num_inference_steps)
+        min_inv_rho = sigma_min ** (1 / rho)
+        max_inv_rho = sigma_max ** (1 / rho)
+        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
+        return sigmas
+
     @property
     def state_in_first_order(self):
         return self.dt is None

tests/schedulers/test_scheduler_heun.py

@@ -129,3 +129,28 @@ class HeunDiscreteSchedulerTest(SchedulerCommonTest):
             # CUDA
             assert abs(result_sum.item() - 0.1233) < 1e-2
             assert abs(result_mean.item() - 0.0002) < 1e-3
+
+    def test_full_loop_device_karras_sigmas(self):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config()
+        scheduler = scheduler_class(**scheduler_config, use_karras_sigmas=True)
+
+        scheduler.set_timesteps(self.num_inference_steps, device=torch_device)
+
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter.to(torch_device) * scheduler.init_noise_sigma
+        sample = sample.to(torch_device)
+
+        for t in scheduler.timesteps:
+            sample = scheduler.scale_model_input(sample, t)
+
+            model_output = model(sample, t)
+
+            output = scheduler.step(model_output, t, sample)
+            sample = output.prev_sample
+
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_sum.item() - 0.00015) < 1e-2
+        assert abs(result_mean.item() - 1.9869554535034695e-07) < 1e-2