def step(
        self,
        model_output: torch.FloatTensor,
        timestep: Union[float, torch.FloatTensor],
        sample: torch.FloatTensor,
        s_churn: float = 0.0,
        s_tmin: float = 0.0,
        s_tmax: float = float("inf"),
        s_noise: float = 1.0,
        generator: Optional[torch.Generator] = None,
        return_dict: bool = True,
    ) -> Union[FlowMatchHeunDiscreteSchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                A current instance of a sample created by the diffusion process.
            s_churn (`float`):
            s_tmin  (`float`):
            s_tmax  (`float`):
            s_noise (`float`, defaults to 1.0):
                Scaling factor for noise added to the sample.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a
                [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] tuple.

        Returns:
            [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`,
                [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] is returned,
                otherwise a tuple is returned where the first element is the sample tensor.
        """

        if (
            isinstance(timestep, int)
            or isinstance(timestep, torch.IntTensor)
            or isinstance(timestep, torch.LongTensor)
        ):
            raise ValueError(
                (
                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                    " `FlowMatchHeunDiscreteScheduler.step()` is not supported. Make sure to pass"
                    " one of the `scheduler.timesteps` as a timestep."
                ),
            )

        if self.step_index is None:
            self._init_step_index(timestep)

        # Upcast to avoid precision issues when computing prev_sample
        sample = sample.to(torch.float32)

        if self.state_in_first_order:
            sigma = self.sigmas[self.step_index]
            sigma_next = self.sigmas[self.step_index + 1]
        else:
            # 2nd order / Heun's method
            sigma = self.sigmas[self.step_index - 1]
            sigma_next = self.sigmas[self.step_index]

        gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

        sigma_hat = sigma * (gamma + 1)

        if gamma > 0:
            noise = randn_tensor(
                model_output.shape, dtype=model_output.dtype, device=model_output.device, generator=generator
            )
            eps = noise * s_noise
            sample = sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

        if self.state_in_first_order:
            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            denoised = sample - model_output * sigma
            # 2. convert to an ODE derivative for 1st order
            derivative = (sample - denoised) / sigma_hat
            # 3. Delta timestep
            dt = sigma_next - sigma_hat

            # store for 2nd order step
            self.prev_derivative = derivative
            self.dt = dt
            self.sample = sample
        else:
            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            denoised = sample - model_output * sigma_next
            # 2. 2nd order / Heun's method
            derivative = (sample - denoised) / sigma_next
            derivative = 0.5 * (self.prev_derivative + derivative)

            # 3. take prev timestep & sample
            dt = self.dt
            sample = self.sample

            # free dt and derivative
            # Note, this puts the scheduler in "first order mode"
            self.prev_derivative = None
            self.dt = None
            self.sample = None

        prev_sample = sample + derivative * dt
        # Cast sample back to model compatible dtype
        prev_sample = prev_sample.to(model_output.dtype)

        # upon completion increase step index by one
        self._step_index += 1

        if not return_dict:
            return (prev_sample,)

        return FlowMatchHeunDiscreteSchedulerOutput(prev_sample=prev_sample)

        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                A current instance of a sample created by the diffusion process.
            s_churn (`float`):
            s_tmin  (`float`):
            s_tmax  (`float`):
            s_noise (`float`, defaults to 1.0):
                Scaling factor for noise added to the sample.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a
                [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] tuple.

        Returns:
            [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`,
                [`~schedulers.scheduling_flow_match_heun_discrete.FlowMatchHeunDiscreteSchedulerOutput`] is returned,
                otherwise a tuple is returned where the first element is the sample tensor.
        
src/diffusers/schedulers/scheduling_flow_match_heun_discrete.py