Add stochastic sampling to FlowMatchEulerDiscreteScheduler (#11369)

* Add stochastic sampling to FlowMatchEulerDiscreteScheduler

This PR adds stochastic sampling to FlowMatchEulerDiscreteScheduler based on Lightricks/LTX-Video@b1aeddd  ltx_video/schedulers/rf.py

* Apply style fixes

* Use config value directly

* Apply style fixes

* Swap order

* Update src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py

Co-authored-by: YiYi Xu <yixu310@gmail.com>

* Update src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py

Co-authored-by: YiYi Xu <yixu310@gmail.com>

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: YiYi Xu <yixu310@gmail.com>

Author: 3 people

src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py

@@ -80,6 +80,8 @@ class FlowMatchEulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
             Whether to use beta sigmas for step sizes in the noise schedule during sampling.
         time_shift_type (`str`, defaults to "exponential"):
             The type of dynamic resolution-dependent timestep shifting to apply. Either "exponential" or "linear".
+        stochastic_sampling (`bool`, defaults to False):
+            Whether to use stochastic sampling.
     """
 
     _compatibles = []
@@ -101,6 +103,7 @@ def __init__(
         use_exponential_sigmas: Optional[bool] = False,
         use_beta_sigmas: Optional[bool] = False,
         time_shift_type: str = "exponential",
+        stochastic_sampling: bool = False,
     ):
         if self.config.use_beta_sigmas and not is_scipy_available():
             raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
@@ -437,13 +440,25 @@ def step(
             lower_mask = sigmas < per_token_sigmas[None] - 1e-6
             lower_sigmas = lower_mask * sigmas
             lower_sigmas, _ = lower_sigmas.max(dim=0)
-            dt = (per_token_sigmas - lower_sigmas)[..., None]
+
+            current_sigma = per_token_sigmas[..., None]
+            next_sigma = lower_sigmas[..., None]
+            dt = current_sigma - next_sigma
         else:
-            sigma = self.sigmas[self.step_index]
-            sigma_next = self.sigmas[self.step_index + 1]
+            sigma_idx = self.step_index
+            sigma = self.sigmas[sigma_idx]
+            sigma_next = self.sigmas[sigma_idx + 1]
+
+            current_sigma = sigma
+            next_sigma = sigma_next
             dt = sigma_next - sigma
 
-        prev_sample = sample + dt * model_output
+        if self.config.stochastic_sampling:
+            x0 = sample - current_sigma * model_output
+            noise = torch.randn_like(sample)
+            prev_sample = (1.0 - next_sigma) * x0 + next_sigma * noise
+        else:
+            prev_sample = sample + dt * model_output
 
         # upon completion increase step index by one
         self._step_index += 1