Added get_velocity function to EulerDiscreteScheduler. (#7733)

* Added get_velocity function to EulerDiscreteScheduler.

* Fix white space on blank lines

* Added copied from statement

* back to the original.

---------
Co-authored-by: Ruining Li <ruining@robots.ox.ac.uk>
Co-authored-by: Sayak Paul <spsayakpaul@gmail.com>

src/diffusers/schedulers/scheduling_euler_discrete.py

@@ -576,5 +576,44 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         noisy_samples = original_samples + noise * sigma
         return noisy_samples
 
+    def get_velocity(
+        self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.FloatTensor
+    ) -> torch.FloatTensor:
+        if (
+            isinstance(timesteps, int)
+            or isinstance(timesteps, torch.IntTensor)
+            or isinstance(timesteps, torch.LongTensor)
+        ):
+            raise ValueError(
+                (
+                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
+                    " `EulerDiscreteScheduler.get_velocity()` is not supported. Make sure to pass"
+                    " one of the `scheduler.timesteps` as a timestep."
+                ),
+            )
+
+        if sample.device.type == "mps" and torch.is_floating_point(timesteps):
+            # mps does not support float64
+            schedule_timesteps = self.timesteps.to(sample.device, dtype=torch.float32)
+            timesteps = timesteps.to(sample.device, dtype=torch.float32)
+        else:
+            schedule_timesteps = self.timesteps.to(sample.device)
+            timesteps = timesteps.to(sample.device)
+
+        step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
+        alphas_cumprod = self.alphas_cumprod.to(sample)
+        sqrt_alpha_prod = alphas_cumprod[step_indices] ** 0.5
+        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
+        while len(sqrt_alpha_prod.shape) < len(sample.shape):
+            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
+
+        sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[step_indices]) ** 0.5
+        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
+        while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
+            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
+
+        velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
+        return velocity
+
     def __len__(self):
         return self.config.num_train_timesteps