def step(
        self,
        model_output: torch.Tensor,
        timestep: Union[float, torch.Tensor],
        sample: torch.Tensor,
        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[EulerDiscreteSchedulerOutput, 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.Tensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.Tensor`):
                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_euler_discrete.EulerDiscreteSchedulerOutput`] or
                tuple.

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

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

        if not self.is_scale_input_called:
            logger.warning(
                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                "See `StableDiffusionPipeline` for a usage example."
            )

        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)

        sigma = 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

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        # NOTE: "original_sample" should not be an expected prediction_type but is left in for
        # backwards compatibility
        if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
            pred_original_sample = model_output
        elif self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma_hat * model_output
        elif self.config.prediction_type == "v_prediction":
            # denoised = model_output * c_out + input * c_skip
            pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        # 2. Convert to an ODE derivative
        derivative = (sample - pred_original_sample) / sigma_hat

        dt = self.sigmas[self.step_index + 1] - sigma_hat

        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,
                pred_original_sample,
            )

        return EulerDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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.Tensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.Tensor`):
                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_euler_discrete.EulerDiscreteSchedulerOutput`] or
                tuple.

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