Add `use_Karras_sigmas` to DPMSolverSinglestepScheduler (#3476)

* add use_karras_sigmas

* add karras test

* add doc

src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py

@@ -117,6 +117,10 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         lower_order_final (`bool`, default `True`):
             whether to use lower-order solvers in the final steps. For singlestep schedulers, we recommend to enable
             this to use up all the function evaluations.
+        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.
         lambda_min_clipped (`float`, default `-inf`):
             the clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for
             cosine (squaredcos_cap_v2) noise schedule.
@@ -150,6 +154,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         algorithm_type: str = "dpmsolver++",
         solver_type: str = "midpoint",
         lower_order_final: bool = True,
+        use_karras_sigmas: Optional[bool] = False,
         lambda_min_clipped: float = -float("inf"),
         variance_type: Optional[str] = None,
     ):
@@ -197,6 +202,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         self.model_outputs = [None] * solver_order
         self.sample = None
         self.order_list = self.get_order_list(num_train_timesteps)
+        self.use_karras_sigmas = use_karras_sigmas
 
     def get_order_list(self, num_inference_steps: int) -> List[int]:
         """
@@ -252,6 +258,14 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             .copy()
             .astype(np.int64)
         )
+
+        if self.use_karras_sigmas:
+            sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+            log_sigmas = np.log(sigmas)
+            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
+            timesteps = np.flip(timesteps).copy().astype(np.int64)
+
         self.timesteps = torch.from_numpy(timesteps).to(device)
         self.model_outputs = [None] * self.config.solver_order
         self.sample = None
@@ -299,6 +313,44 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
 
         return sample
 
+    # 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
+
     def convert_model_output(
         self, model_output: torch.FloatTensor, timestep: int, sample: torch.FloatTensor
     ) -> torch.FloatTensor:

tests/schedulers/test_scheduler_dpm_single.py

@@ -215,12 +215,24 @@ class DPMSolverSinglestepSchedulerTest(SchedulerCommonTest):
 
         assert abs(result_mean.item() - 0.2791) < 1e-3
 
+    def test_full_loop_with_karras(self):
+        sample = self.full_loop(use_karras_sigmas=True)
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.2248) < 1e-3
+
     def test_full_loop_with_v_prediction(self):
         sample = self.full_loop(prediction_type="v_prediction")
         result_mean = torch.mean(torch.abs(sample))
 
         assert abs(result_mean.item() - 0.1453) < 1e-3
 
+    def test_full_loop_with_karras_and_v_prediction(self):
+        sample = self.full_loop(prediction_type="v_prediction", use_karras_sigmas=True)
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.0649) < 1e-3
+
     def test_fp16_support(self):
         scheduler_class = self.scheduler_classes[0]
         scheduler_config = self.get_scheduler_config(thresholding=True, dynamic_thresholding_ratio=0)