[`Cont'd`] Add the SDE variant of ~~DPM-Solver~~ and DPM-Solver++ to DPM Single Step (#8269)

* Add the SDE variant of DPM-Solver and DPM-Solver++ to DPM Single Step


---------
Co-authored-by: cmdr2 <secondary.cmdr2@gmail.com>

src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py

@@ -22,6 +22,7 @@ import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import deprecate, logging
+from ..utils.torch_utils import randn_tensor
 from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
 
 
@@ -108,11 +109,11 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
             `algorithm_type="dpmsolver++"`.
         algorithm_type (`str`, defaults to `dpmsolver++`):
-            Algorithm type for the solver; can be `dpmsolver` or `dpmsolver++`. The `dpmsolver` type implements the
-            algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927) paper, and the `dpmsolver++` type
-            implements the algorithms in the [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is
-            recommended to use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling like in
-            Stable Diffusion.
+            Algorithm type for the solver; can be `dpmsolver` or `dpmsolver++` or `sde-dpmsolver++`. The `dpmsolver`
+            type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927) paper, and the
+            `dpmsolver++` type implements the algorithms in the [DPMSolver++](https://huggingface.co/papers/2211.01095)
+            paper. It is recommended to use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided
+            sampling like in Stable Diffusion.
         solver_type (`str`, defaults to `midpoint`):
             Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
             sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
@@ -186,7 +187,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         self.init_noise_sigma = 1.0
 
         # settings for DPM-Solver
-        if algorithm_type not in ["dpmsolver", "dpmsolver++"]:
+        if algorithm_type not in ["dpmsolver", "dpmsolver++", "sde-dpmsolver++"]:
             if algorithm_type == "deis":
                 self.register_to_config(algorithm_type="dpmsolver++")
             else:
@@ -197,7 +198,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             else:
                 raise NotImplementedError(f"{solver_type} is not implemented for {self.__class__}")
 
-        if algorithm_type != "dpmsolver++" and final_sigmas_type == "zero":
+        if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"] and final_sigmas_type == "zero":
             raise ValueError(
                 f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please chooose `sigma_min` instead."
             )
@@ -493,10 +494,10 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
                 "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
             )
         # DPM-Solver++ needs to solve an integral of the data prediction model.
-        if self.config.algorithm_type == "dpmsolver++":
+        if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
             if self.config.prediction_type == "epsilon":
                 # DPM-Solver and DPM-Solver++ only need the "mean" output.
-                if self.config.variance_type in ["learned_range"]:
+                if self.config.variance_type in ["learned", "learned_range"]:
                     model_output = model_output[:, :3]
                 sigma = self.sigmas[self.step_index]
                 alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
@@ -517,34 +518,43 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
                 x0_pred = self._threshold_sample(x0_pred)
 
             return x0_pred
+
         # DPM-Solver needs to solve an integral of the noise prediction model.
         elif self.config.algorithm_type == "dpmsolver":
             if self.config.prediction_type == "epsilon":
                 # DPM-Solver and DPM-Solver++ only need the "mean" output.
-                if self.config.variance_type in ["learned_range"]:
-                    model_output = model_output[:, :3]
-                return model_output
+                if self.config.variance_type in ["learned", "learned_range"]:
+                    epsilon = model_output[:, :3]
+                else:
+                    epsilon = model_output
             elif self.config.prediction_type == "sample":
                 sigma = self.sigmas[self.step_index]
                 alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                 epsilon = (sample - alpha_t * model_output) / sigma_t
-                return epsilon
             elif self.config.prediction_type == "v_prediction":
                 sigma = self.sigmas[self.step_index]
                 alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                 epsilon = alpha_t * model_output + sigma_t * sample
-                return epsilon
             else:
                 raise ValueError(
                     f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                     " `v_prediction` for the DPMSolverSinglestepScheduler."
                 )
 
+            if self.config.thresholding:
+                alpha_t, sigma_t = self.alpha_t[timestep], self.sigma_t[timestep]
+                x0_pred = (sample - sigma_t * epsilon) / alpha_t
+                x0_pred = self._threshold_sample(x0_pred)
+                epsilon = (sample - alpha_t * x0_pred) / sigma_t
+
+            return epsilon
+
     def dpm_solver_first_order_update(
         self,
         model_output: torch.Tensor,
         *args,
         sample: torch.Tensor = None,
+        noise: Optional[torch.Tensor] = None,
         **kwargs,
     ) -> torch.Tensor:
         """
@@ -594,6 +604,13 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output
         elif self.config.algorithm_type == "dpmsolver":
             x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
+        elif self.config.algorithm_type == "sde-dpmsolver++":
+            assert noise is not None
+            x_t = (
+                (sigma_t / sigma_s * torch.exp(-h)) * sample
+                + (alpha_t * (1 - torch.exp(-2.0 * h))) * model_output
+                + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+            )
         return x_t
 
     def singlestep_dpm_solver_second_order_update(
@@ -601,6 +618,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         model_output_list: List[torch.Tensor],
         *args,
         sample: torch.Tensor = None,
+        noise: Optional[torch.Tensor] = None,
         **kwargs,
     ) -> torch.Tensor:
         """
@@ -688,6 +706,22 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
                     - (sigma_t * (torch.exp(h) - 1.0)) * D0
                     - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                 )
+        elif self.config.algorithm_type == "sde-dpmsolver++":
+            assert noise is not None
+            if self.config.solver_type == "midpoint":
+                x_t = (
+                    (sigma_t / sigma_s1 * torch.exp(-h)) * sample
+                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
+                    + 0.5 * (alpha_t * (1 - torch.exp(-2.0 * h))) * D1
+                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+                )
+            elif self.config.solver_type == "heun":
+                x_t = (
+                    (sigma_t / sigma_s1 * torch.exp(-h)) * sample
+                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
+                    + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1
+                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
+                )
         return x_t
 
     def singlestep_dpm_solver_third_order_update(
@@ -800,6 +834,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         *args,
         sample: torch.Tensor = None,
         order: int = None,
+        noise: Optional[torch.Tensor] = None,
         **kwargs,
     ) -> torch.Tensor:
         """
@@ -848,9 +883,9 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             )
 
         if order == 1:
-            return self.dpm_solver_first_order_update(model_output_list[-1], sample=sample)
+            return self.dpm_solver_first_order_update(model_output_list[-1], sample=sample, noise=noise)
         elif order == 2:
-            return self.singlestep_dpm_solver_second_order_update(model_output_list, sample=sample)
+            return self.singlestep_dpm_solver_second_order_update(model_output_list, sample=sample, noise=noise)
         elif order == 3:
             return self.singlestep_dpm_solver_third_order_update(model_output_list, sample=sample)
         else:
@@ -894,6 +929,7 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         model_output: torch.Tensor,
         timestep: int,
         sample: torch.Tensor,
+        generator=None,
         return_dict: bool = True,
     ) -> Union[SchedulerOutput, Tuple]:
         """
@@ -929,6 +965,13 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
             self.model_outputs[i] = self.model_outputs[i + 1]
         self.model_outputs[-1] = model_output
 
+        if self.config.algorithm_type == "sde-dpmsolver++":
+            noise = randn_tensor(
+                model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
+            )
+        else:
+            noise = None
+
         order = self.order_list[self.step_index]
 
         #  For img2img denoising might start with order>1 which is not possible
@@ -940,9 +983,11 @@ class DPMSolverSinglestepScheduler(SchedulerMixin, ConfigMixin):
         if order == 1:
             self.sample = sample
 
-        prev_sample = self.singlestep_dpm_solver_update(self.model_outputs, sample=self.sample, order=order)
+        prev_sample = self.singlestep_dpm_solver_update(
+            self.model_outputs, sample=self.sample, order=order, noise=noise
+        )
 
-        # upon completion increase step index by one
+        # upon completion increase step index by one, noise=noise
         self._step_index += 1
 
         if not return_dict:

tests/schedulers/test_scheduler_dpm_single.py

@@ -194,10 +194,14 @@ class DPMSolverSinglestepSchedulerTest(SchedulerCommonTest):
             self.check_over_configs(prediction_type=prediction_type)
 
     def test_solver_order_and_type(self):
-        for algorithm_type in ["dpmsolver", "dpmsolver++"]:
+        for algorithm_type in ["dpmsolver", "dpmsolver++", "sde-dpmsolver++"]:
             for solver_type in ["midpoint", "heun"]:
                 for order in [1, 2, 3]:
                     for prediction_type in ["epsilon", "sample"]:
+                        if algorithm_type == "sde-dpmsolver++":
+                            if order == 3:
+                                continue
+                        else:
                             self.check_over_configs(
                                 solver_order=order,
                                 solver_type=solver_type,