def step(
        self,
        model_output: torch.Tensor,
        timestep: Union[float, torch.Tensor],
        sample: torch.Tensor,
        generator: Optional[torch.Generator] = None,
        return_dict: bool = True,
    ) -> Union[EulerAncestralDiscreteSchedulerOutput, 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.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a
                [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or tuple.

        Returns:
            [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or `tuple`:
                If return_dict is `True`,
                [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] 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)

        sigma = self.sigmas[self.step_index]

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

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma * model_output
        elif self.config.prediction_type == "v_prediction":
            # * c_out + input * c_skip
            pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
        elif self.config.prediction_type == "sample":
            raise NotImplementedError("prediction_type not implemented yet: sample")
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        sigma_from = self.sigmas[self.step_index]
        sigma_to = self.sigmas[self.step_index + 1]
        sigma_up = (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
        sigma_down = (sigma_to**2 - sigma_up**2) ** 0.5

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

        dt = sigma_down - sigma

        prev_sample = sample + derivative * dt

        device = model_output.device
        noise = randn_tensor(model_output.shape, dtype=model_output.dtype, device=device, generator=generator)

        prev_sample = prev_sample + noise * sigma_up

        # 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 EulerAncestralDiscreteSchedulerOutput(
            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.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a
                [`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or tuple.

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

        
src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py