DPMSolverMultistepInverse

DPMSolverMultistepInverse is the inverted 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.

The implementation is mostly based on the DDIM inversion definition of Null-text Inversion for Editing Real Images using Guided Diffusion Models and notebook implementation of the DiffEdit latent inversion from Xiang-cd/DiffEdit-stable-diffusion.

Tips

Dynamic thresholding from Imagen is supported, and for pixel-space diffusion models, you can set both algorithm_type="dpmsolver++" and thresholding=True to use the dynamic thresholding. This thresholding method is unsuitable for latent-space diffusion models such as Stable Diffusion.

mindone.diffusers.DPMSolverMultistepInverseScheduler

Bases: SchedulerMixin, ConfigMixin

DPMSolverMultistepInverseScheduler is the reverse scheduler of [DPMSolverMultistepScheduler].

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
num_train_timesteps	The number of diffusion steps to train the model. TYPE: `int`, defaults to 1000 DEFAULT: 1000
beta_start	The starting beta value of inference. TYPE: `float`, defaults to 0.0001 DEFAULT: 0.0001
beta_end	The final beta value. TYPE: `float`, defaults to 0.02 DEFAULT: 0.02
beta_schedule	The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from linear, scaled_linear, or squaredcos_cap_v2. TYPE: `str`, defaults to `"linear"` DEFAULT: 'linear'
trained_betas	Pass an array of betas directly to the constructor to bypass beta_start and beta_end. TYPE: `np.ndarray`, *optional* DEFAULT: None
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, dpmsolver++, sde-dpmsolver or sde-dpmsolver++. The dpmsolver type implements the algorithms in the DPMSolver paper, and 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
use_karras_sigmas	Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If True, the sigmas are determined according to a sequence of noise levels {σi}. TYPE: `bool`, *optional*, defaults to `False` DEFAULT: False
lambda_min_clipped	Clipping threshold for the minimum value of lambda(t) for numerical stability. This is critical for the cosine (squaredcos_cap_v2) noise schedule. TYPE: `float`, defaults to `-inf` DEFAULT: -float('inf')
variance_type	Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output contains the predicted Gaussian variance. TYPE: `str`, *optional* DEFAULT: None
timestep_spacing	The way the timesteps should be scaled. Refer to Table 2 of the Common Diffusion Noise Schedules and Sample Steps are Flawed for more information. TYPE: `str`, defaults to `"linspace"` DEFAULT: 'linspace'
steps_offset	An offset added to the inference steps, as required by some model families. TYPE: `int`, defaults to 0 DEFAULT: 0

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

class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
    """
    `DPMSolverMultistepInverseScheduler` is the reverse scheduler of [`DPMSolverMultistepScheduler`].

    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:
        num_train_timesteps (`int`, defaults to 1000):
            The number of diffusion steps to train the model.
        beta_start (`float`, defaults to 0.0001):
            The starting `beta` value of inference.
        beta_end (`float`, defaults to 0.02):
            The final `beta` value.
        beta_schedule (`str`, defaults to `"linear"`):
            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
        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`, `dpmsolver++`, `sde-dpmsolver` or `sde-dpmsolver++`. The
            `dpmsolver` type implements the algorithms in the [DPMSolver](https://huggingface.co/papers/2206.00927)
            paper, and 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.
        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
            Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
            the sigmas are determined according to a sequence of noise levels {σi}.
        lambda_min_clipped (`float`, defaults to `-inf`):
            Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
            cosine (`squaredcos_cap_v2`) noise schedule.
        variance_type (`str`, *optional*):
            Set to "learned" or "learned_range" for diffusion models that predict variance. If set, the model's output
            contains the predicted Gaussian variance.
        timestep_spacing (`str`, defaults to `"linspace"`):
            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
        steps_offset (`int`, defaults to 0):
            An offset added to the inference steps, as required by some model families.
    """

    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        solver_order: int = 2,
        prediction_type: str = "epsilon",
        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,
        use_karras_sigmas: Optional[bool] = False,
        lambda_min_clipped: float = -float("inf"),
        variance_type: Optional[str] = None,
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
    ):
        if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
            deprecation_message = (
                f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. "
                "Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
            )
            deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0", deprecation_message)

        if trained_betas is not None:
            self.betas = ms.tensor(trained_betas, dtype=ms.float32)
        elif beta_schedule == "linear":
            self.betas = ms.tensor(np.linspace(beta_start, beta_end, num_train_timesteps), dtype=ms.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = (
                ms.tensor(np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps), dtype=ms.float32) ** 2
            )
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = ops.cumprod(self.alphas, dim=0)
        # Currently we only support VP-type noise schedule
        self.alpha_t = ops.sqrt(self.alphas_cumprod)
        self.sigma_t = ops.sqrt(1 - self.alphas_cumprod)
        self.lambda_t = ops.log(self.alpha_t) - ops.log(self.sigma_t)
        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

        # settings for DPM-Solver
        if algorithm_type not in ["dpmsolver", "dpmsolver++", "sde-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__}")

        # setable values
        self.num_inference_steps = None
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32).copy()
        self.timesteps = ms.tensor(timesteps)
        self.model_outputs = [None] * solver_order
        self.lower_order_nums = 0
        self._step_index = None
        self.use_karras_sigmas = use_karras_sigmas

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

    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.
        """
        # Clipping the minimum of all lambda(t) for numerical stability.
        # This is critical for cosine (squaredcos_cap_v2) noise schedule.
        clipped_idx = ms.tensor(
            np.searchsorted(ops.flip(self.lambda_t, [0]).asnumpy(), self.config.lambda_min_clipped)
        ).item()
        self.noisiest_timestep = self.config.num_train_timesteps - 1 - clipped_idx

        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
            timesteps = (
                np.linspace(0, self.noisiest_timestep, num_inference_steps + 1).round()[:-1].copy().astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = (self.noisiest_timestep + 1) // (num_inference_steps + 1)
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[:-1].copy().astype(np.int64)
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = np.arange(self.noisiest_timestep + 1, 0, -step_ratio).round()[::-1].copy().astype(np.int64)
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', "
                "'leading' or 'trailing'."
            )

        sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).asnumpy()
        log_sigmas = np.log(sigmas)

        if self.config.use_karras_sigmas:
            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
            timesteps = timesteps.copy().astype(np.int64)
            sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            sigma_max = (
                (1 - self.alphas_cumprod[self.noisiest_timestep]) / self.alphas_cumprod[self.noisiest_timestep]
            ) ** 0.5
            sigmas = np.concatenate([sigmas, [sigma_max]]).astype(np.float32)

        self.sigmas = ms.Tensor(sigmas)

        # when num_inference_steps == num_train_timesteps, we can end up with
        # duplicates in timesteps.
        _, unique_indices = np.unique(timesteps, return_index=True)
        timesteps = timesteps[np.sort(unique_indices)]

        self.timesteps = ms.tensor(timesteps, dtype=ms.int64)

        self.num_inference_steps = len(timesteps)

        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

    # 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

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
    def _sigma_to_alpha_sigma_t(self, sigma):
        alpha_t = 1 / ((sigma**2 + 1) ** 0.5)
        sigma_t = sigma * alpha_t

        return alpha_t, sigma_t

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
    def _convert_to_karras(self, in_sigmas: ms.Tensor, num_inference_steps) -> ms.Tensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        # Hack to make sure that other schedulers which copy this function don't break
        # TODO: Add this logic to the other schedulers
        if hasattr(self.config, "sigma_min"):
            sigma_min = self.config.sigma_min
        else:
            sigma_min = None

        if hasattr(self.config, "sigma_max"):
            sigma_max = self.config.sigma_max
        else:
            sigma_max = None

        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()

        rho = 7.0  # 7.0 is the value used in the paper
        ramp = np.linspace(0, 1, num_inference_steps)
        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_dpmsolver_multistep.DPMSolverMultistepScheduler.convert_model_output
    def convert_model_output(
        self,
        model_output: ms.Tensor,
        *args,
        sample: ms.Tensor = None,
        **kwargs,
    ) -> 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.
        """
        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError("missing `sample` as a required keyward argument")
        if timestep is not None:
            deprecate(
                "timesteps",
                "1.0.0",
                "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        # DPM-Solver++ needs to solve an integral of the data prediction model.
        if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
            if self.config.prediction_type == "epsilon":
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned", "learned_range"]:
                    model_output = model_output[:, :3]
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                x0_pred = ((sample - sigma_t.to(model_output.dtype) * model_output) / alpha_t).to(sample.dtype)
            elif self.config.prediction_type == "sample":
                x0_pred = model_output
            elif self.config.prediction_type == "v_prediction":
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                x0_pred = alpha_t.to(sample.dtype) * sample - sigma_t.to(model_output.dtype) * model_output
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the DPMSolverMultistepScheduler."
                )

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

            return x0_pred

        # DPM-Solver needs to solve an integral of the noise prediction model.
        elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
            if self.config.prediction_type == "epsilon":
                # DPM-Solver and DPM-Solver++ only need the "mean" output.
                if self.config.variance_type in ["learned", "learned_range"]:
                    epsilon = model_output[:, :3]
                else:
                    epsilon = model_output
            elif self.config.prediction_type == "sample":
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                epsilon = (sample - alpha_t * model_output) / sigma_t
            elif self.config.prediction_type == "v_prediction":
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                epsilon = alpha_t * model_output + sigma_t * sample
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the DPMSolverMultistepScheduler."
                )

            if self.config.thresholding:
                sigma = self.sigmas[self.step_index]
                alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
                x0_pred = (sample - sigma_t * epsilon) / alpha_t
                x0_pred = self._threshold_sample(x0_pred)
                epsilon = (sample - alpha_t * x0_pred) / sigma_t

            return epsilon

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.dpm_solver_first_order_update
    def dpm_solver_first_order_update(
        self,
        model_output: ms.Tensor,
        *args,
        sample: ms.Tensor = None,
        noise: Optional[ms.Tensor] = None,
        **kwargs,
    ) -> 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
        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing `sample` as a required keyward argument")
        if timestep is not None:
            deprecate(
                "timesteps",
                "1.0.0",
                "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        if prev_timestep is not None:
            deprecate(
                "prev_timestep",
                "1.0.0",
                "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

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

        return x_t

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update
    def multistep_dpm_solver_second_order_update(
        self,
        model_output_list: List[ms.Tensor],
        *args,
        sample: ms.Tensor = None,
        noise: Optional[ms.Tensor] = None,
        **kwargs,
    ) -> 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
        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing `sample` as a required keyward argument")
        if timestep_list is not None:
            deprecate(
                "timestep_list",
                "1.0.0",
                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        if prev_timestep is not None:
            deprecate(
                "prev_timestep",
                "1.0.0",
                "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        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(m0.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 == "dpmsolver":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            if self.config.solver_type == "midpoint":
                x_t = (
                    (alpha_t / alpha_s0).to(dtype) * sample
                    - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
                    - 0.5 * (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D1
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (alpha_t / alpha_s0).to(dtype) * sample
                    - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
                    - (sigma_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
                )
        elif self.config.algorithm_type == "sde-dpmsolver":
            assert noise is not None
            if self.config.solver_type == "midpoint":
                x_t = (
                    (alpha_t / alpha_s0).to(dtype) * sample
                    - (2.0 * (sigma_t * (ops.exp(h) - 1.0))).to(dtype) * D0
                    - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D1
                    + (sigma_t * ops.sqrt(ops.exp(2 * h) - 1.0)).to(dtype) * noise
                )
            elif self.config.solver_type == "heun":
                x_t = (
                    (alpha_t / alpha_s0).to(dtype) * sample
                    - (2.0 * (sigma_t * (ops.exp(h) - 1.0))).to(dtype) * D0
                    - (2.0 * (sigma_t * ((ops.exp(h) - 1.0) / h - 1.0))).to(dtype) * D1
                    + (sigma_t * ops.sqrt(ops.exp(2 * h) - 1.0)).to(dtype) * noise
                )
        return x_t

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update
    def multistep_dpm_solver_third_order_update(
        self,
        model_output_list: List[ms.Tensor],
        *args,
        sample: ms.Tensor = None,
        **kwargs,
    ) -> 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
        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 2:
                sample = args[2]
            else:
                raise ValueError(" missing`sample` as a required keyward argument")
        if timestep_list is not None:
            deprecate(
                "timestep_list",
                "1.0.0",
                "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        if prev_timestep is not None:
            deprecate(
                "prev_timestep",
                "1.0.0",
                "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        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
            )
        elif self.config.algorithm_type == "dpmsolver":
            # See https://arxiv.org/abs/2206.00927 for detailed derivations
            x_t = (
                (alpha_t / alpha_s0).to(dtype) * sample
                - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
                - (sigma_t * ((ops.exp(h) - 1.0) / h - 1.0)).to(dtype) * D1
                - (sigma_t * ((ops.exp(h) - 1.0 - h) / h**2 - 0.5)).to(dtype) * D2
            )
        return x_t

    def _init_step_index(self, timestep):
        index_candidates_num = (self.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((self.timesteps == timestep).nonzero()[pos])

        self._step_index = step_index

    def step(
        self,
        model_output: ms.Tensor,
        timestep: Union[int, ms.Tensor],
        sample: ms.Tensor,
        generator=None,
        variance_noise: Optional[ms.Tensor] = 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.
            variance_noise (`ms.Tensor`):
                Alternative to generating noise with `generator` by directly providing the noise for the variance
                itself. Useful for methods such as [`CycleDiffusion`].
            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)
        )
        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 in ["sde-dpmsolver", "sde-dpmsolver++"] and variance_noise is None:
            noise = randn_tensor(model_output.shape, generator=generator, dtype=model_output.dtype)
        elif self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
            noise = variance_noise
        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_dpmsolver_multistep.DPMSolverMultistepScheduler.scale_model_input
    def scale_model_input(self, sample: ms.Tensor, *args, **kwargs) -> ms.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`ms.Tensor`):
                The input sample.

        Returns:
            `ms.Tensor`:
                A scaled input sample.
        """
        return sample

    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

        step_indices = []
        for timestep in timesteps:
            index_candidates_num = (schedule_timesteps == timestep).sum()
            if index_candidates_num == 0:
                step_index = len(schedule_timesteps) - 1
            else:
                if index_candidates_num > 1:
                    pos = 1
                else:
                    pos = 0
                step_index = int((schedule_timesteps == timestep).nonzero()[pos])
            step_indices.append(step_index)

        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))

        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
        return noisy_samples

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

mindone.diffusers.DPMSolverMultistepInverseScheduler.step_index property

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

mindone.diffusers.DPMSolverMultistepInverseScheduler.convert_model_output(model_output, *args, sample=None, **kwargs)

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_dpmsolver_multistep_inverse.py

def convert_model_output(
    self,
    model_output: ms.Tensor,
    *args,
    sample: ms.Tensor = None,
    **kwargs,
) -> 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.
    """
    timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
    if sample is None:
        if len(args) > 1:
            sample = args[1]
        else:
            raise ValueError("missing `sample` as a required keyward argument")
    if timestep is not None:
        deprecate(
            "timesteps",
            "1.0.0",
            "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    # DPM-Solver++ needs to solve an integral of the data prediction model.
    if self.config.algorithm_type in ["dpmsolver++", "sde-dpmsolver++"]:
        if self.config.prediction_type == "epsilon":
            # DPM-Solver and DPM-Solver++ only need the "mean" output.
            if self.config.variance_type in ["learned", "learned_range"]:
                model_output = model_output[:, :3]
            sigma = self.sigmas[self.step_index]
            alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
            x0_pred = ((sample - sigma_t.to(model_output.dtype) * model_output) / alpha_t).to(sample.dtype)
        elif self.config.prediction_type == "sample":
            x0_pred = model_output
        elif self.config.prediction_type == "v_prediction":
            sigma = self.sigmas[self.step_index]
            alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
            x0_pred = alpha_t.to(sample.dtype) * sample - sigma_t.to(model_output.dtype) * model_output
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                " `v_prediction` for the DPMSolverMultistepScheduler."
            )

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

        return x0_pred

    # DPM-Solver needs to solve an integral of the noise prediction model.
    elif self.config.algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
        if self.config.prediction_type == "epsilon":
            # DPM-Solver and DPM-Solver++ only need the "mean" output.
            if self.config.variance_type in ["learned", "learned_range"]:
                epsilon = model_output[:, :3]
            else:
                epsilon = model_output
        elif self.config.prediction_type == "sample":
            sigma = self.sigmas[self.step_index]
            alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
            epsilon = (sample - alpha_t * model_output) / sigma_t
        elif self.config.prediction_type == "v_prediction":
            sigma = self.sigmas[self.step_index]
            alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
            epsilon = alpha_t * model_output + sigma_t * sample
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                " `v_prediction` for the DPMSolverMultistepScheduler."
            )

        if self.config.thresholding:
            sigma = self.sigmas[self.step_index]
            alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
            x0_pred = (sample - sigma_t * epsilon) / alpha_t
            x0_pred = self._threshold_sample(x0_pred)
            epsilon = (sample - alpha_t * x0_pred) / sigma_t

        return epsilon

mindone.diffusers.DPMSolverMultistepInverseScheduler.dpm_solver_first_order_update(model_output, *args, sample=None, noise=None, **kwargs)

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_dpmsolver_multistep_inverse.py

def dpm_solver_first_order_update(
    self,
    model_output: ms.Tensor,
    *args,
    sample: ms.Tensor = None,
    noise: Optional[ms.Tensor] = None,
    **kwargs,
) -> 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
    timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
    prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
    if sample is None:
        if len(args) > 2:
            sample = args[2]
        else:
            raise ValueError(" missing `sample` as a required keyward argument")
    if timestep is not None:
        deprecate(
            "timesteps",
            "1.0.0",
            "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    if prev_timestep is not None:
        deprecate(
            "prev_timestep",
            "1.0.0",
            "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

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

    return x_t

mindone.diffusers.DPMSolverMultistepInverseScheduler.multistep_dpm_solver_second_order_update(model_output_list, *args, sample=None, noise=None, **kwargs)

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_dpmsolver_multistep_inverse.py

def multistep_dpm_solver_second_order_update(
    self,
    model_output_list: List[ms.Tensor],
    *args,
    sample: ms.Tensor = None,
    noise: Optional[ms.Tensor] = None,
    **kwargs,
) -> 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
    timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
    prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
    if sample is None:
        if len(args) > 2:
            sample = args[2]
        else:
            raise ValueError(" missing `sample` as a required keyward argument")
    if timestep_list is not None:
        deprecate(
            "timestep_list",
            "1.0.0",
            "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    if prev_timestep is not None:
        deprecate(
            "prev_timestep",
            "1.0.0",
            "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    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(m0.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 == "dpmsolver":
        # See https://arxiv.org/abs/2206.00927 for detailed derivations
        if self.config.solver_type == "midpoint":
            x_t = (
                (alpha_t / alpha_s0).to(dtype) * sample
                - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
                - 0.5 * (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D1
            )
        elif self.config.solver_type == "heun":
            x_t = (
                (alpha_t / alpha_s0).to(dtype) * sample
                - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
                - (sigma_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
            )
    elif self.config.algorithm_type == "sde-dpmsolver":
        assert noise is not None
        if self.config.solver_type == "midpoint":
            x_t = (
                (alpha_t / alpha_s0).to(dtype) * sample
                - (2.0 * (sigma_t * (ops.exp(h) - 1.0))).to(dtype) * D0
                - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D1
                + (sigma_t * ops.sqrt(ops.exp(2 * h) - 1.0)).to(dtype) * noise
            )
        elif self.config.solver_type == "heun":
            x_t = (
                (alpha_t / alpha_s0).to(dtype) * sample
                - (2.0 * (sigma_t * (ops.exp(h) - 1.0))).to(dtype) * D0
                - (2.0 * (sigma_t * ((ops.exp(h) - 1.0) / h - 1.0))).to(dtype) * D1
                + (sigma_t * ops.sqrt(ops.exp(2 * h) - 1.0)).to(dtype) * noise
            )
    return x_t

mindone.diffusers.DPMSolverMultistepInverseScheduler.multistep_dpm_solver_third_order_update(model_output_list, *args, sample=None, **kwargs)

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_dpmsolver_multistep_inverse.py

def multistep_dpm_solver_third_order_update(
    self,
    model_output_list: List[ms.Tensor],
    *args,
    sample: ms.Tensor = None,
    **kwargs,
) -> 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
    timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
    prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None)
    if sample is None:
        if len(args) > 2:
            sample = args[2]
        else:
            raise ValueError(" missing`sample` as a required keyward argument")
    if timestep_list is not None:
        deprecate(
            "timestep_list",
            "1.0.0",
            "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    if prev_timestep is not None:
        deprecate(
            "prev_timestep",
            "1.0.0",
            "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    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
        )
    elif self.config.algorithm_type == "dpmsolver":
        # See https://arxiv.org/abs/2206.00927 for detailed derivations
        x_t = (
            (alpha_t / alpha_s0).to(dtype) * sample
            - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * D0
            - (sigma_t * ((ops.exp(h) - 1.0) / h - 1.0)).to(dtype) * D1
            - (sigma_t * ((ops.exp(h) - 1.0 - h) / h**2 - 0.5)).to(dtype) * D2
        )
    return x_t

mindone.diffusers.DPMSolverMultistepInverseScheduler.scale_model_input(sample, *args, **kwargs)

Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep.

PARAMETER	DESCRIPTION
sample	The input sample. TYPE: `ms.Tensor`

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

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

def scale_model_input(self, sample: ms.Tensor, *args, **kwargs) -> ms.Tensor:
    """
    Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
    current timestep.

    Args:
        sample (`ms.Tensor`):
            The input sample.

    Returns:
        `ms.Tensor`:
            A scaled input sample.
    """
    return sample

mindone.diffusers.DPMSolverMultistepInverseScheduler.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_dpmsolver_multistep_inverse.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.
    """
    # Clipping the minimum of all lambda(t) for numerical stability.
    # This is critical for cosine (squaredcos_cap_v2) noise schedule.
    clipped_idx = ms.tensor(
        np.searchsorted(ops.flip(self.lambda_t, [0]).asnumpy(), self.config.lambda_min_clipped)
    ).item()
    self.noisiest_timestep = self.config.num_train_timesteps - 1 - clipped_idx

    # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
    if self.config.timestep_spacing == "linspace":
        timesteps = (
            np.linspace(0, self.noisiest_timestep, num_inference_steps + 1).round()[:-1].copy().astype(np.int64)
        )
    elif self.config.timestep_spacing == "leading":
        step_ratio = (self.noisiest_timestep + 1) // (num_inference_steps + 1)
        # creates integer timesteps by multiplying by ratio
        # casting to int to avoid issues when num_inference_step is power of 3
        timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[:-1].copy().astype(np.int64)
        timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
        step_ratio = self.config.num_train_timesteps / num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # casting to int to avoid issues when num_inference_step is power of 3
        timesteps = np.arange(self.noisiest_timestep + 1, 0, -step_ratio).round()[::-1].copy().astype(np.int64)
        timesteps -= 1
    else:
        raise ValueError(
            f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', "
            "'leading' or 'trailing'."
        )

    sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).asnumpy()
    log_sigmas = np.log(sigmas)

    if self.config.use_karras_sigmas:
        sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
        timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
        timesteps = timesteps.copy().astype(np.int64)
        sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
    else:
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        sigma_max = (
            (1 - self.alphas_cumprod[self.noisiest_timestep]) / self.alphas_cumprod[self.noisiest_timestep]
        ) ** 0.5
        sigmas = np.concatenate([sigmas, [sigma_max]]).astype(np.float32)

    self.sigmas = ms.Tensor(sigmas)

    # when num_inference_steps == num_train_timesteps, we can end up with
    # duplicates in timesteps.
    _, unique_indices = np.unique(timesteps, return_index=True)
    timesteps = timesteps[np.sort(unique_indices)]

    self.timesteps = ms.tensor(timesteps, dtype=ms.int64)

    self.num_inference_steps = len(timesteps)

    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

mindone.diffusers.DPMSolverMultistepInverseScheduler.step(model_output, timestep, sample, generator=None, variance_noise=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
variance_noise	Alternative to generating noise with generator by directly providing the noise for the variance itself. Useful for methods such as [CycleDiffusion]. TYPE: `ms.Tensor` 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_dpmsolver_multistep_inverse.py

def step(
    self,
    model_output: ms.Tensor,
    timestep: Union[int, ms.Tensor],
    sample: ms.Tensor,
    generator=None,
    variance_noise: Optional[ms.Tensor] = 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.
        variance_noise (`ms.Tensor`):
            Alternative to generating noise with `generator` by directly providing the noise for the variance
            itself. Useful for methods such as [`CycleDiffusion`].
        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)
    )
    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 in ["sde-dpmsolver", "sde-dpmsolver++"] and variance_noise is None:
        noise = randn_tensor(model_output.shape, generator=generator, dtype=model_output.dtype)
    elif self.config.algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
        noise = variance_noise
    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)