EDMDPMSolverMultistepScheduler

EDMDPMSolverMultistepScheduler is a Karras formulation of DPMSolverMultistepScheduler, a multistep scheduler from DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps and DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models by Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu.

DPMSolver (and the improved version DPMSolver++) is a fast dedicated high-order solver for diffusion ODEs with convergence order guarantee. Empirically, DPMSolver sampling with only 20 steps can generate high-quality samples, and it can generate quite good samples even in 10 steps.

mindone.diffusers.EDMDPMSolverMultistepScheduler

Bases: SchedulerMixin, ConfigMixin

Implements DPMSolverMultistepScheduler in EDM formulation as presented in Karras et al. 2022 [1]. EDMDPMSolverMultistepScheduler is a fast dedicated high-order solver for diffusion ODEs.

[1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models." https://arxiv.org/abs/2206.00364

This model inherits from [SchedulerMixin] and [ConfigMixin]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.

PARAMETER	DESCRIPTION
sigma_min	Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the EDM paper [1]; a reasonable range is [0, 10]. TYPE: `float`, *optional*, defaults to 0.002 DEFAULT: 0.002
sigma_max	Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the EDM paper [1]; a reasonable range is [0.2, 80.0]. TYPE: `float`, *optional*, defaults to 80.0 DEFAULT: 80.0
sigma_data	The standard deviation of the data distribution. This is set to 0.5 in the EDM paper [1]. TYPE: `float`, *optional*, defaults to 0.5 DEFAULT: 0.5
sigma_schedule	Sigma schedule to compute the sigmas. By default, we the schedule introduced in the EDM paper (https://arxiv.org/abs/2206.00364). Other acceptable value is "exponential". The exponential schedule was incorporated in this model: https://huggingface.co/stabilityai/cosxl. TYPE: `str`, *optional*, defaults to `karras` DEFAULT: 'karras'
num_train_timesteps	The number of diffusion steps to train the model. TYPE: `int`, defaults to 1000 DEFAULT: 1000
solver_order	The DPMSolver order which can be 1 or 2 or 3. It is recommended to use solver_order=2 for guided sampling, and solver_order=3 for unconditional sampling. TYPE: `int`, defaults to 2 DEFAULT: 2
prediction_type	Prediction type of the scheduler function; can be epsilon (predicts the noise of the diffusion process), sample (directly predicts the noisy sample) orv_prediction` (see section 2.4 of Imagen Video paper). TYPE: `str`, defaults to `epsilon`, *optional* DEFAULT: 'epsilon'
thresholding	Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such as Stable Diffusion. TYPE: `bool`, defaults to `False` DEFAULT: False
dynamic_thresholding_ratio	The ratio for the dynamic thresholding method. Valid only when thresholding=True. TYPE: `float`, defaults to 0.995 DEFAULT: 0.995
sample_max_value	The threshold value for dynamic thresholding. Valid only when thresholding=True and algorithm_type="dpmsolver++". TYPE: `float`, defaults to 1.0 DEFAULT: 1.0
algorithm_type	Algorithm type for the solver; can be dpmsolver++ or sde-dpmsolver++. The dpmsolver++ type implements the algorithms in the DPMSolver++ paper. It is recommended to use dpmsolver++ or sde-dpmsolver++ with solver_order=2 for guided sampling like in Stable Diffusion. TYPE: `str`, defaults to `dpmsolver++` DEFAULT: 'dpmsolver++'
solver_type	Solver type for the second-order solver; can be midpoint or heun. The solver type slightly affects the sample quality, especially for a small number of steps. It is recommended to use midpoint solvers. TYPE: `str`, defaults to `midpoint` DEFAULT: 'midpoint'
lower_order_final	Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10. TYPE: `bool`, defaults to `True` DEFAULT: True
euler_at_final	Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference steps, but sometimes may result in blurring. TYPE: `bool`, defaults to `False` DEFAULT: False
final_sigmas_type	The final sigma value for the noise schedule during the sampling process. If "sigma_min", the final sigma is the same as the last sigma in the training schedule. If zero, the final sigma is set to 0. TYPE: `str`, defaults to `"zero"` DEFAULT: 'zero'

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

class EDMDPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
    Implements DPMSolverMultistepScheduler in EDM formulation as presented in Karras et al. 2022 [1].
    `EDMDPMSolverMultistepScheduler` is a fast dedicated high-order solver for diffusion ODEs.

    [1] Karras, Tero, et al. "Elucidating the Design Space of Diffusion-Based Generative Models."
    https://arxiv.org/abs/2206.00364

    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
    methods the library implements for all schedulers such as loading and saving.

    Args:
        sigma_min (`float`, *optional*, defaults to 0.002):
            Minimum noise magnitude in the sigma schedule. This was set to 0.002 in the EDM paper [1]; a reasonable
            range is [0, 10].
        sigma_max (`float`, *optional*, defaults to 80.0):
            Maximum noise magnitude in the sigma schedule. This was set to 80.0 in the EDM paper [1]; a reasonable
            range is [0.2, 80.0].
        sigma_data (`float`, *optional*, defaults to 0.5):
            The standard deviation of the data distribution. This is set to 0.5 in the EDM paper [1].
        sigma_schedule (`str`, *optional*, defaults to `karras`):
            Sigma schedule to compute the `sigmas`. By default, we the schedule introduced in the EDM paper
            (https://arxiv.org/abs/2206.00364). Other acceptable value is "exponential". The exponential schedule was
            incorporated in this model: https://huggingface.co/stabilityai/cosxl.
        num_train_timesteps (`int`, defaults to 1000):
            The number of diffusion steps to train the model.
        solver_order (`int`, defaults to 2):
            The DPMSolver order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
            sampling, and `solver_order=3` for unconditional sampling.
        prediction_type (`str`, defaults to `epsilon`, *optional*):
            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
            Video](https://imagen.research.google/video/paper.pdf) paper).
        thresholding (`bool`, defaults to `False`):
            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
            as Stable Diffusion.
        dynamic_thresholding_ratio (`float`, defaults to 0.995):
            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
        sample_max_value (`float`, defaults to 1.0):
            The threshold value for dynamic thresholding. Valid only when `thresholding=True` and
            `algorithm_type="dpmsolver++"`.
        algorithm_type (`str`, defaults to `dpmsolver++`):
            Algorithm type for the solver; can be `dpmsolver++` or `sde-dpmsolver++`. The `dpmsolver++` type implements
            the algorithms in the [DPMSolver++](https://huggingface.co/papers/2211.01095) paper. It is recommended to
            use `dpmsolver++` or `sde-dpmsolver++` with `solver_order=2` for guided sampling like in Stable Diffusion.
        solver_type (`str`, defaults to `midpoint`):
            Solver type for the second-order solver; can be `midpoint` or `heun`. The solver type slightly affects the
            sample quality, especially for a small number of steps. It is recommended to use `midpoint` solvers.
        lower_order_final (`bool`, defaults to `True`):
            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. This can
            stabilize the sampling of DPMSolver for steps < 15, especially for steps <= 10.
        euler_at_final (`bool`, defaults to `False`):
            Whether to use Euler's method in the final step. It is a trade-off between numerical stability and detail
            richness. This can stabilize the sampling of the SDE variant of DPMSolver for small number of inference
            steps, but sometimes may result in blurring.
        final_sigmas_type (`str`, defaults to `"zero"`):
            The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
            sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
    """

    _compatibles = []
    order = 1

    @register_to_config
    def __init__(
        self,
        sigma_min: float = 0.002,
        sigma_max: float = 80.0,
        sigma_data: float = 0.5,
        sigma_schedule: str = "karras",
        num_train_timesteps: int = 1000,
        prediction_type: str = "epsilon",
        rho: float = 7.0,
        solver_order: int = 2,
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        sample_max_value: float = 1.0,
        algorithm_type: str = "dpmsolver++",
        solver_type: str = "midpoint",
        lower_order_final: bool = True,
        euler_at_final: bool = False,
        final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
    ):
        # settings for DPM-Solver
        if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"]:
            if algorithm_type == "deis":
                self.register_to_config(algorithm_type="dpmsolver++")
            else:
                raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}")

        if solver_type not in ["midpoint", "heun"]:
            if solver_type in ["logrho", "bh1", "bh2"]:
                self.register_to_config(solver_type="midpoint")
            else:
                raise NotImplementedError(f"{solver_type} is not implemented for {self.__class__}")

        if algorithm_type not in ["dpmsolver++", "sde-dpmsolver++"] and final_sigmas_type == "zero":
            raise ValueError(
                f"`final_sigmas_type` {final_sigmas_type} is not supported for `algorithm_type` {algorithm_type}. Please choose `sigma_min` instead."
            )

        ramp = ms.tensor(np.linspace(0, 1, num_train_timesteps), dtype=ms.float32)
        if sigma_schedule == "karras":
            sigmas = self._compute_karras_sigmas(ramp)
        elif sigma_schedule == "exponential":
            sigmas = self._compute_exponential_sigmas(ramp)

        self.timesteps = self.precondition_noise(sigmas)

        self.sigmas = ops.cat([sigmas, ops.zeros(1, dtype=sigmas.dtype)])

        # setable values
        self.num_inference_steps = None
        self.model_outputs = [None] * solver_order
        self.lower_order_nums = 0
        self._step_index = None
        self._begin_index = None
        self.sigma_data = self.config.sigma_data

    @property
    def init_noise_sigma(self):
        # standard deviation of the initial noise distribution
        return (self.config.sigma_max**2 + 1) ** 0.5

    @property
    def step_index(self):
        """
        The index counter for current timestep. It will increase 1 after each scheduler step.
        """
        return self._step_index

    @property
    def begin_index(self):
        """
        The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
        """
        return self._begin_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
    def set_begin_index(self, begin_index: int = 0):
        """
        Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

        Args:
            begin_index (`int`):
                The begin index for the scheduler.
        """
        self._begin_index = begin_index

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.precondition_inputs
    def precondition_inputs(self, sample, sigma):
        c_in = 1 / ((sigma**2 + self.sigma_data**2) ** 0.5)
        scaled_sample = (sample * c_in).to(sample.dtype)
        return scaled_sample

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.precondition_noise
    def precondition_noise(self, sigma):
        if not isinstance(sigma, ms.Tensor):
            sigma = ms.tensor(sigma)

        c_noise = 0.25 * ops.log(sigma)

        return c_noise

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.precondition_outputs
    def precondition_outputs(self, sample, model_output, sigma):
        sigma_data = self.sigma_data
        c_skip = sigma_data**2 / (sigma**2 + sigma_data**2)

        if self.config.prediction_type == "epsilon":
            c_out = sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
        elif self.config.prediction_type == "v_prediction":
            c_out = -sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
        else:
            raise ValueError(f"Prediction type {self.config.prediction_type} is not supported.")

        denoised = c_skip.to(sample.dtype) * sample + c_out.to(sample.dtype) * model_output

        return denoised

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler.scale_model_input
    def scale_model_input(self, sample: ms.Tensor, timestep: Union[float, ms.Tensor]) -> ms.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.

        Args:
            sample (`ms.Tensor`):
                The input sample.
            timestep (`int`, *optional*):
                The current timestep in the diffusion chain.

        Returns:
            `ms.Tensor`:
                A scaled input sample.
        """
        if self.step_index is None:
            self._init_step_index(timestep)

        sigma = self.sigmas[self.step_index]
        sample = self.precondition_inputs(sample, sigma)

        self.is_scale_input_called = True
        return sample

    def set_timesteps(self, num_inference_steps: int = None):
        """
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).

        Args:
            num_inference_steps (`int`):
                The number of diffusion steps used when generating samples with a pre-trained model.
        """

        self.num_inference_steps = num_inference_steps

        ramp = ms.tensor(np.linspace(0, 1, self.num_inference_steps))
        if self.config.sigma_schedule == "karras":
            sigmas = self._compute_karras_sigmas(ramp)
        elif self.config.sigma_schedule == "exponential":
            sigmas = self._compute_exponential_sigmas(ramp)

        sigmas = sigmas.to(ms.float32)
        self.timesteps = self.precondition_noise(sigmas)

        if self.config.final_sigmas_type == "sigma_min":
            sigma_last = self.config.sigma_min
        elif self.config.final_sigmas_type == "zero":
            sigma_last = 0
        else:
            raise ValueError(
                f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
            )

        self.sigmas = ops.cat([sigmas, ms.tensor([sigma_last], dtype=ms.float32)])

        self.model_outputs = [
            None,
        ] * self.config.solver_order
        self.lower_order_nums = 0

        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None
        self._begin_index = None

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler._compute_karras_sigmas
    def _compute_karras_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> ms.Tensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        sigma_min = sigma_min or self.config.sigma_min
        sigma_max = sigma_max or self.config.sigma_max

        rho = self.config.rho
        min_inv_rho = sigma_min ** (1 / rho)
        max_inv_rho = sigma_max ** (1 / rho)
        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
        return sigmas

    # Copied from diffusers.schedulers.scheduling_edm_euler.EDMEulerScheduler._compute_exponential_sigmas
    def _compute_exponential_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> ms.Tensor:
        """Implementation closely follows k-diffusion.

        https://github.com/crowsonkb/k-diffusion/blob/6ab5146d4a5ef63901326489f31f1d8e7dd36b48/k_diffusion/sampling.py#L26
        """
        sigma_min = sigma_min or self.config.sigma_min
        sigma_max = sigma_max or self.config.sigma_max
        sigmas = ms.tensor(np.linspace(math.log(sigma_min), math.log(sigma_max), len(ramp))).exp().flip((0,))
        return sigmas

    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: ms.Tensor) -> ms.Tensor:
        """
        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
        photorealism as well as better image-text alignment, especially when using very large guidance weights."

        https://arxiv.org/abs/2205.11487
        """
        dtype = sample.dtype
        batch_size, channels, *remaining_dims = sample.shape

        if dtype not in (ms.float32, ms.float64):
            sample = sample.float()  # upcast for quantile calculation, and clamp not implemented for cpu half

        # Flatten sample for doing quantile calculation along each image
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims).item())

        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"

        s = ms.Tensor.from_numpy(np.quantile(abs_sample.asnumpy(), self.config.dynamic_thresholding_ratio, axis=1))
        s = ops.clamp(
            s, min=1, max=self.config.sample_max_value
        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
        s = s.unsqueeze(1)  # (batch_size, 1) because clamp will broadcast along dim=0
        sample = ops.clamp(sample, -s, s) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"

        sample = sample.reshape(batch_size, channels, *remaining_dims)
        sample = sample.to(dtype)

        return sample

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
    def _sigma_to_t(self, sigma, log_sigmas):
        # get log sigma
        log_sigma = np.log(np.maximum(sigma, 1e-10))

        # get distribution
        dists = log_sigma - log_sigmas[:, np.newaxis]

        # get sigmas range
        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
        high_idx = low_idx + 1

        low = log_sigmas[low_idx]
        high = log_sigmas[high_idx]

        # interpolate sigmas
        w = (low - log_sigma) / (low - high)
        w = np.clip(w, 0, 1)

        # transform interpolation to time range
        t = (1 - w) * low_idx + w * high_idx
        t = t.reshape(sigma.shape)
        return t

    def _sigma_to_alpha_sigma_t(self, sigma):
        alpha_t = ms.tensor(1, dtype=ms.float32)  # Inputs are pre-scaled before going into unet, so alpha_t = 1
        sigma_t = sigma

        return alpha_t, sigma_t

    def convert_model_output(
        self,
        model_output: ms.Tensor,
        sample: ms.Tensor = None,
    ) -> ms.Tensor:
        """
        Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
        designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
        integral of the data prediction model.

        <Tip>

        The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
        prediction and data prediction models.

        </Tip>

        Args:
            model_output (`ms.Tensor`):
                The direct output from the learned diffusion model.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.

        Returns:
            `ms.Tensor`:
                The converted model output.
        """
        sigma = self.sigmas[self.step_index]
        x0_pred = self.precondition_outputs(sample, model_output, sigma)

        if self.config.thresholding:
            x0_pred = self._threshold_sample(x0_pred)

        return x0_pred

    def dpm_solver_first_order_update(
        self,
        model_output: ms.Tensor,
        sample: ms.Tensor = None,
        noise: Optional[ms.Tensor] = None,
    ) -> ms.Tensor:
        """
        One step for the first-order DPMSolver (equivalent to DDIM).

        Args:
            model_output (`ms.Tensor`):
                The direct output from the learned diffusion model.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.

        Returns:
            `ms.Tensor`:
                The sample tensor at the previous timestep.
        """
        dtype = sample.dtype
        sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
        lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
        lambda_s = ops.log(alpha_s) - ops.log(sigma_s)

        h = lambda_t - lambda_s
        if self.config.algorithm_type == "dpmsolver++":
            x_t = (sigma_t / sigma_s).to(dtype) * sample - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * model_output
        elif self.config.algorithm_type == "sde-dpmsolver++":
            assert noise is not None
            x_t = (
                (sigma_t / sigma_s * ops.exp(-h)).to(dtype) * sample
                + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * model_output
                + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
            )

        return x_t

    def multistep_dpm_solver_second_order_update(
        self,
        model_output_list: List[ms.Tensor],
        sample: ms.Tensor = None,
        noise: Optional[ms.Tensor] = None,
    ) -> ms.Tensor:
        """
        One step for the second-order multistep DPMSolver.

        Args:
            model_output_list (`List[ms.Tensor]`):
                The direct outputs from learned diffusion model at current and latter timesteps.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.

        Returns:
            `ms.Tensor`:
                The sample tensor at the previous timestep.
        """
        dtype = sample.dtype
        sigma_t, sigma_s0, sigma_s1 = (
            self.sigmas[self.step_index + 1],
            self.sigmas[self.step_index],
            self.sigmas[self.step_index - 1],
        )

        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)

        lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
        lambda_s0 = ops.log(alpha_s0) - ops.log(sigma_s0)
        lambda_s1 = ops.log(alpha_s1) - ops.log(sigma_s1)

        m0, m1 = model_output_list[-1], model_output_list[-2]

        h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1
        r0 = h_0 / h
        D0, D1 = m0, (1.0 / r0).to(dtype) * (m0 - m1)
        if self.config.algorithm_type == "dpmsolver++":
            # See https://arxiv.org/abs/2211.01095 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (sigma_t / sigma_s0).to(dtype) * sample
                    - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
                    - (0.5 * (alpha_t * (ops.exp(-h) - 1.0))).to(dtype) * D1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (sigma_t / sigma_s0).to(dtype) * sample
                    - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
                    + (alpha_t * ((ops.exp(-h) - 1.0) / h + 1.0)).to(dtype) * D1
                )
        elif self.config.algorithm_type == "sde-dpmsolver++":
            assert noise is not None
            if self.config.solver_type == "midpoint":
                x_t = (
                    (sigma_t / sigma_s0 * ops.exp(-h)).to(dtype) * sample
                    + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * D0
                    + (0.5 * (alpha_t * (1 - ops.exp(-2.0 * h)))).to(dtype) * D1
                    + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (sigma_t / sigma_s0 * ops.exp(-h)).to(dtype) * sample
                    + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * D0
                    + (alpha_t * ((1.0 - ops.exp(-2.0 * h)) / (-2.0 * h) + 1.0)).to(dtype) * D1
                    + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
                )

        return x_t

    def multistep_dpm_solver_third_order_update(
        self,
        model_output_list: List[ms.Tensor],
        sample: ms.Tensor = None,
    ) -> ms.Tensor:
        """
        One step for the third-order multistep DPMSolver.

        Args:
            model_output_list (`List[ms.Tensor]`):
                The direct outputs from learned diffusion model at current and latter timesteps.
            sample (`ms.Tensor`):
                A current instance of a sample created by diffusion process.

        Returns:
            `ms.Tensor`:
                The sample tensor at the previous timestep.
        """
        dtype = sample.dtype
        sigma_t, sigma_s0, sigma_s1, sigma_s2 = (
            self.sigmas[self.step_index + 1],
            self.sigmas[self.step_index],
            self.sigmas[self.step_index - 1],
            self.sigmas[self.step_index - 2],
        )

        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
        alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
        alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)

        lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
        lambda_s0 = ops.log(alpha_s0) - ops.log(sigma_s0)
        lambda_s1 = ops.log(alpha_s1) - ops.log(sigma_s1)
        lambda_s2 = ops.log(alpha_s2) - ops.log(sigma_s2)

        m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]

        h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2
        r0, r1 = h_0 / h, h_1 / h
        D0 = m0
        D1_0, D1_1 = (1.0 / r0).to(dtype) * (m0 - m1), (1.0 / r1).to(dtype) * (m1 - m2)
        D1 = D1_0 + (r0 / (r0 + r1)).to(dtype) * (D1_0 - D1_1)
        D2 = (1.0 / (r0 + r1)).to(dtype) * (D1_0 - D1_1)
        if self.config.algorithm_type == "dpmsolver++":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            x_t = (
                (sigma_t / sigma_s0).to(dtype) * sample
                - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
                + (alpha_t * ((ops.exp(-h) - 1.0) / h + 1.0)).to(dtype) * D1
                - (alpha_t * ((ops.exp(-h) - 1.0 + h) / h**2 - 0.5)).to(dtype) * D2
            )

        return x_t

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep
    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps

        index_candidates_num = (schedule_timesteps == timestep).sum()

        if index_candidates_num == 0:
            step_index = len(self.timesteps) - 1
        # The sigma index that is taken for the **very** first `step`
        # is always the second index (or the last index if there is only 1)
        # This way we can ensure we don't accidentally skip a sigma in
        # case we start in the middle of the denoising schedule (e.g. for image-to-image)
        else:
            if index_candidates_num > 1:
                pos = 1
            else:
                pos = 0
            step_index = int((schedule_timesteps == timestep).nonzero()[pos])

        return step_index

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
    def _init_step_index(self, timestep):
        """
        Initialize the step_index counter for the scheduler.
        """

        if self.begin_index is None:
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index

    def step(
        self,
        model_output: ms.Tensor,
        timestep: int,
        sample: ms.Tensor,
        generator=None,
        return_dict: bool = False,
    ) -> Union[SchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
        the multistep DPMSolver.

        Args:
            model_output (`ms.Tensor`):
                The direct output from learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.
            generator (`np.random.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.

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

        """
        if self.num_inference_steps is None:
            raise ValueError(
                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
            )

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

        # Improve numerical stability for small number of steps
        lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
            self.config.euler_at_final
            or (self.config.lower_order_final and len(self.timesteps) < 15)
            or self.config.final_sigmas_type == "zero"
        )
        lower_order_second = (
            (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
        )

        model_output = self.convert_model_output(model_output, sample=sample)
        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
        self.model_outputs[-1] = model_output

        if self.config.algorithm_type == "sde-dpmsolver++":
            noise = randn_tensor(model_output.shape, generator=generator, dtype=model_output.dtype)
        else:
            noise = None

        if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
            prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise)
        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
            prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise)
        else:
            prev_sample = self.multistep_dpm_solver_third_order_update(self.model_outputs, sample=sample)

        if self.lower_order_nums < self.config.solver_order:
            self.lower_order_nums += 1

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

        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
    def add_noise(
        self,
        original_samples: ms.Tensor,
        noise: ms.Tensor,
        timesteps: ms.Tensor,
    ) -> ms.Tensor:
        broadcast_shape = original_samples.shape
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        sigmas = self.sigmas.to(dtype=original_samples.dtype)
        schedule_timesteps = self.timesteps

        # self.begin_index is None when scheduler is used for training, or pipeline does not implement set_begin_index
        if self.begin_index is None:
            step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
        elif self.step_index is not None:
            # add_noise is called after first denoising step (for inpainting)
            step_indices = [self.step_index] * timesteps.shape[0]
        else:
            # add noise is called bevore first denoising step to create inital latent(img2img)
            step_indices = [self.begin_index] * timesteps.shape[0]

        sigma = sigmas[step_indices].flatten()
        # while len(sigma.shape) < len(original_samples.shape):
        #     sigma = sigma.unsqueeze(-1)
        sigma = ops.reshape(sigma, (timesteps.shape[0],) + (1,) * (len(broadcast_shape) - 1))

        noisy_samples = original_samples + noise * sigma
        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps

mindone.diffusers.EDMDPMSolverMultistepScheduler.begin_index property

The index for the first timestep. It should be set from pipeline with set_begin_index method.

mindone.diffusers.EDMDPMSolverMultistepScheduler.step_index property

The index counter for current timestep. It will increase 1 after each scheduler step.

mindone.diffusers.EDMDPMSolverMultistepScheduler.convert_model_output(model_output, sample=None)

Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an integral of the data prediction model.

The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise prediction and data prediction models.

PARAMETER	DESCRIPTION
model_output	The direct output from the learned diffusion model. TYPE: `ms.Tensor`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor` DEFAULT: None

RETURNS	DESCRIPTION
Tensor	ms.Tensor: The converted model output.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def convert_model_output(
    self,
    model_output: ms.Tensor,
    sample: ms.Tensor = None,
) -> ms.Tensor:
    """
    Convert the model output to the corresponding type the DPMSolver/DPMSolver++ algorithm needs. DPM-Solver is
    designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an
    integral of the data prediction model.

    <Tip>

    The algorithm and model type are decoupled. You can use either DPMSolver or DPMSolver++ for both noise
    prediction and data prediction models.

    </Tip>

    Args:
        model_output (`ms.Tensor`):
            The direct output from the learned diffusion model.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.

    Returns:
        `ms.Tensor`:
            The converted model output.
    """
    sigma = self.sigmas[self.step_index]
    x0_pred = self.precondition_outputs(sample, model_output, sigma)

    if self.config.thresholding:
        x0_pred = self._threshold_sample(x0_pred)

    return x0_pred

mindone.diffusers.EDMDPMSolverMultistepScheduler.dpm_solver_first_order_update(model_output, sample=None, noise=None)

One step for the first-order DPMSolver (equivalent to DDIM).

PARAMETER	DESCRIPTION
model_output	The direct output from the learned diffusion model. TYPE: `ms.Tensor`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor` DEFAULT: None

RETURNS	DESCRIPTION
Tensor	ms.Tensor: The sample tensor at the previous timestep.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def dpm_solver_first_order_update(
    self,
    model_output: ms.Tensor,
    sample: ms.Tensor = None,
    noise: Optional[ms.Tensor] = None,
) -> ms.Tensor:
    """
    One step for the first-order DPMSolver (equivalent to DDIM).

    Args:
        model_output (`ms.Tensor`):
            The direct output from the learned diffusion model.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.

    Returns:
        `ms.Tensor`:
            The sample tensor at the previous timestep.
    """
    dtype = sample.dtype
    sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
    alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
    alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
    lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
    lambda_s = ops.log(alpha_s) - ops.log(sigma_s)

    h = lambda_t - lambda_s
    if self.config.algorithm_type == "dpmsolver++":
        x_t = (sigma_t / sigma_s).to(dtype) * sample - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * model_output
    elif self.config.algorithm_type == "sde-dpmsolver++":
        assert noise is not None
        x_t = (
            (sigma_t / sigma_s * ops.exp(-h)).to(dtype) * sample
            + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * model_output
            + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
        )

    return x_t

mindone.diffusers.EDMDPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update(model_output_list, sample=None, noise=None)

One step for the second-order multistep DPMSolver.

PARAMETER	DESCRIPTION
model_output_list	The direct outputs from learned diffusion model at current and latter timesteps. TYPE: `List[ms.Tensor]`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor` DEFAULT: None

RETURNS	DESCRIPTION
Tensor	ms.Tensor: The sample tensor at the previous timestep.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def multistep_dpm_solver_second_order_update(
    self,
    model_output_list: List[ms.Tensor],
    sample: ms.Tensor = None,
    noise: Optional[ms.Tensor] = None,
) -> ms.Tensor:
    """
    One step for the second-order multistep DPMSolver.

    Args:
        model_output_list (`List[ms.Tensor]`):
            The direct outputs from learned diffusion model at current and latter timesteps.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.

    Returns:
        `ms.Tensor`:
            The sample tensor at the previous timestep.
    """
    dtype = sample.dtype
    sigma_t, sigma_s0, sigma_s1 = (
        self.sigmas[self.step_index + 1],
        self.sigmas[self.step_index],
        self.sigmas[self.step_index - 1],
    )

    alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
    alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
    alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)

    lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
    lambda_s0 = ops.log(alpha_s0) - ops.log(sigma_s0)
    lambda_s1 = ops.log(alpha_s1) - ops.log(sigma_s1)

    m0, m1 = model_output_list[-1], model_output_list[-2]

    h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1
    r0 = h_0 / h
    D0, D1 = m0, (1.0 / r0).to(dtype) * (m0 - m1)
    if self.config.algorithm_type == "dpmsolver++":
        # See https://arxiv.org/abs/2211.01095 for detailed derivations
        if self.config.solver_type == "midpoint":
            x_t = (
                (sigma_t / sigma_s0).to(dtype) * sample
                - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
                - (0.5 * (alpha_t * (ops.exp(-h) - 1.0))).to(dtype) * D1
            )
        elif self.config.solver_type == "heun":
            x_t = (
                (sigma_t / sigma_s0).to(dtype) * sample
                - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
                + (alpha_t * ((ops.exp(-h) - 1.0) / h + 1.0)).to(dtype) * D1
            )
    elif self.config.algorithm_type == "sde-dpmsolver++":
        assert noise is not None
        if self.config.solver_type == "midpoint":
            x_t = (
                (sigma_t / sigma_s0 * ops.exp(-h)).to(dtype) * sample
                + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * D0
                + (0.5 * (alpha_t * (1 - ops.exp(-2.0 * h)))).to(dtype) * D1
                + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
            )
        elif self.config.solver_type == "heun":
            x_t = (
                (sigma_t / sigma_s0 * ops.exp(-h)).to(dtype) * sample
                + (alpha_t * (1 - ops.exp(-2.0 * h))).to(dtype) * D0
                + (alpha_t * ((1.0 - ops.exp(-2.0 * h)) / (-2.0 * h) + 1.0)).to(dtype) * D1
                + (sigma_t * ops.sqrt(1.0 - ops.exp(-2 * h))).to(dtype) * noise
            )

    return x_t

mindone.diffusers.EDMDPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update(model_output_list, sample=None)

One step for the third-order multistep DPMSolver.

PARAMETER	DESCRIPTION
model_output_list	The direct outputs from learned diffusion model at current and latter timesteps. TYPE: `List[ms.Tensor]`
sample	A current instance of a sample created by diffusion process. TYPE: `ms.Tensor` DEFAULT: None

RETURNS	DESCRIPTION
Tensor	ms.Tensor: The sample tensor at the previous timestep.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def multistep_dpm_solver_third_order_update(
    self,
    model_output_list: List[ms.Tensor],
    sample: ms.Tensor = None,
) -> ms.Tensor:
    """
    One step for the third-order multistep DPMSolver.

    Args:
        model_output_list (`List[ms.Tensor]`):
            The direct outputs from learned diffusion model at current and latter timesteps.
        sample (`ms.Tensor`):
            A current instance of a sample created by diffusion process.

    Returns:
        `ms.Tensor`:
            The sample tensor at the previous timestep.
    """
    dtype = sample.dtype
    sigma_t, sigma_s0, sigma_s1, sigma_s2 = (
        self.sigmas[self.step_index + 1],
        self.sigmas[self.step_index],
        self.sigmas[self.step_index - 1],
        self.sigmas[self.step_index - 2],
    )

    alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
    alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
    alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1)
    alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2)

    lambda_t = ops.log(alpha_t) - ops.log(sigma_t)
    lambda_s0 = ops.log(alpha_s0) - ops.log(sigma_s0)
    lambda_s1 = ops.log(alpha_s1) - ops.log(sigma_s1)
    lambda_s2 = ops.log(alpha_s2) - ops.log(sigma_s2)

    m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]

    h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2
    r0, r1 = h_0 / h, h_1 / h
    D0 = m0
    D1_0, D1_1 = (1.0 / r0).to(dtype) * (m0 - m1), (1.0 / r1).to(dtype) * (m1 - m2)
    D1 = D1_0 + (r0 / (r0 + r1)).to(dtype) * (D1_0 - D1_1)
    D2 = (1.0 / (r0 + r1)).to(dtype) * (D1_0 - D1_1)
    if self.config.algorithm_type == "dpmsolver++":
        # See https://arxiv.org/abs/2206.00927 for detailed derivations
        x_t = (
            (sigma_t / sigma_s0).to(dtype) * sample
            - (alpha_t * (ops.exp(-h) - 1.0)).to(dtype) * D0
            + (alpha_t * ((ops.exp(-h) - 1.0) / h + 1.0)).to(dtype) * D1
            - (alpha_t * ((ops.exp(-h) - 1.0 + h) / h**2 - 0.5)).to(dtype) * D2
        )

    return x_t

mindone.diffusers.EDMDPMSolverMultistepScheduler.scale_model_input(sample, timestep)

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Scales the denoising model input by (sigma**2 + 1) ** 0.5 to match the Euler algorithm.

PARAMETER	DESCRIPTION
sample	The input sample. TYPE: `ms.Tensor`
timestep	The current timestep in the diffusion chain. TYPE: `int`, *optional*

RETURNS	DESCRIPTION
Tensor	ms.Tensor: A scaled input sample.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def scale_model_input(self, sample: ms.Tensor, timestep: Union[float, ms.Tensor]) -> ms.Tensor:
    """
    Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
    current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.

    Args:
        sample (`ms.Tensor`):
            The input sample.
        timestep (`int`, *optional*):
            The current timestep in the diffusion chain.

    Returns:
        `ms.Tensor`:
            A scaled input sample.
    """
    if self.step_index is None:
        self._init_step_index(timestep)

    sigma = self.sigmas[self.step_index]
    sample = self.precondition_inputs(sample, sigma)

    self.is_scale_input_called = True
    return sample

mindone.diffusers.EDMDPMSolverMultistepScheduler.set_begin_index(begin_index=0)

Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

PARAMETER	DESCRIPTION
begin_index	The begin index for the scheduler. TYPE: `int` DEFAULT: 0

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def set_begin_index(self, begin_index: int = 0):
    """
    Sets the begin index for the scheduler. This function should be run from pipeline before the inference.

    Args:
        begin_index (`int`):
            The begin index for the scheduler.
    """
    self._begin_index = begin_index

mindone.diffusers.EDMDPMSolverMultistepScheduler.set_timesteps(num_inference_steps=None)

Sets the discrete timesteps used for the diffusion chain (to be run before inference).

PARAMETER	DESCRIPTION
num_inference_steps	The number of diffusion steps used when generating samples with a pre-trained model. TYPE: `int` DEFAULT: None

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def set_timesteps(self, num_inference_steps: int = None):
    """
    Sets the discrete timesteps used for the diffusion chain (to be run before inference).

    Args:
        num_inference_steps (`int`):
            The number of diffusion steps used when generating samples with a pre-trained model.
    """

    self.num_inference_steps = num_inference_steps

    ramp = ms.tensor(np.linspace(0, 1, self.num_inference_steps))
    if self.config.sigma_schedule == "karras":
        sigmas = self._compute_karras_sigmas(ramp)
    elif self.config.sigma_schedule == "exponential":
        sigmas = self._compute_exponential_sigmas(ramp)

    sigmas = sigmas.to(ms.float32)
    self.timesteps = self.precondition_noise(sigmas)

    if self.config.final_sigmas_type == "sigma_min":
        sigma_last = self.config.sigma_min
    elif self.config.final_sigmas_type == "zero":
        sigma_last = 0
    else:
        raise ValueError(
            f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}"
        )

    self.sigmas = ops.cat([sigmas, ms.tensor([sigma_last], dtype=ms.float32)])

    self.model_outputs = [
        None,
    ] * self.config.solver_order
    self.lower_order_nums = 0

    # add an index counter for schedulers that allow duplicated timesteps
    self._step_index = None
    self._begin_index = None

mindone.diffusers.EDMDPMSolverMultistepScheduler.step(model_output, timestep, sample, generator=None, return_dict=False)

Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the multistep DPMSolver.

PARAMETER	DESCRIPTION
model_output	The direct output from learned diffusion model. TYPE: `ms.Tensor`
timestep	The current discrete timestep in the diffusion chain. TYPE: `int`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor`
generator	A random number generator. TYPE: `np.random.Generator`, *optional* DEFAULT: None
return_dict	Whether or not to return a [~schedulers.scheduling_utils.SchedulerOutput] or tuple. TYPE: `bool` DEFAULT: False

RETURNS	DESCRIPTION
Union[SchedulerOutput, Tuple]	[~schedulers.scheduling_utils.SchedulerOutput] or tuple: If return_dict is True, [~schedulers.scheduling_utils.SchedulerOutput] is returned, otherwise a tuple is returned where the first element is the sample tensor.

Source code in mindone/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py

def step(
    self,
    model_output: ms.Tensor,
    timestep: int,
    sample: ms.Tensor,
    generator=None,
    return_dict: bool = False,
) -> Union[SchedulerOutput, Tuple]:
    """
    Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with
    the multistep DPMSolver.

    Args:
        model_output (`ms.Tensor`):
            The direct output from learned diffusion model.
        timestep (`int`):
            The current discrete timestep in the diffusion chain.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.
        generator (`np.random.Generator`, *optional*):
            A random number generator.
        return_dict (`bool`):
            Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.

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

    """
    if self.num_inference_steps is None:
        raise ValueError(
            "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
        )

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

    # Improve numerical stability for small number of steps
    lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
        self.config.euler_at_final
        or (self.config.lower_order_final and len(self.timesteps) < 15)
        or self.config.final_sigmas_type == "zero"
    )
    lower_order_second = (
        (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
    )

    model_output = self.convert_model_output(model_output, sample=sample)
    for i in range(self.config.solver_order - 1):
        self.model_outputs[i] = self.model_outputs[i + 1]
    self.model_outputs[-1] = model_output

    if self.config.algorithm_type == "sde-dpmsolver++":
        noise = randn_tensor(model_output.shape, generator=generator, dtype=model_output.dtype)
    else:
        noise = None

    if self.config.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
        prev_sample = self.dpm_solver_first_order_update(model_output, sample=sample, noise=noise)
    elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
        prev_sample = self.multistep_dpm_solver_second_order_update(self.model_outputs, sample=sample, noise=noise)
    else:
        prev_sample = self.multistep_dpm_solver_third_order_update(self.model_outputs, sample=sample)

    if self.lower_order_nums < self.config.solver_order:
        self.lower_order_nums += 1

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

    if not return_dict:
        return (prev_sample,)

    return SchedulerOutput(prev_sample=prev_sample)