UniPCMultistepScheduler

UniPCMultistepScheduler is a training-free framework designed for fast sampling of diffusion models. It was introduced in UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models by Wenliang Zhao, Lujia Bai, Yongming Rao, Jie Zhou, Jiwen Lu.

It consists of a corrector (UniC) and a predictor (UniP) that share a unified analytical form and support arbitrary orders. UniPC is by design model-agnostic, supporting pixel-space/latent-space DPMs on unconditional/conditional sampling. It can also be applied to both noise prediction and data prediction models. The corrector UniC can be also applied after any off-the-shelf solvers to increase the order of accuracy.

The abstract from the paper is:

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM is time-consuming due to the multiple evaluations of the denoising network, making it more and more important to accelerate the sampling of DPMs. Despite recent progress in designing fast samplers, existing methods still cannot generate satisfying images in many applications where fewer steps (e.g., <10) are favored. In this paper, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods, especially in extremely few steps. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256×256 (conditional) with only 10 function evaluations. Code is available at this https URL.

Tips

It is recommended to set solver_order to 2 for guide sampling, and solver_order=3 for unconditional sampling.

Dynamic thresholding from Imagen is supported, and for pixel-space diffusion models, you can set both predict_x0=True and thresholding=True to use dynamic thresholding. This thresholding method is unsuitable for latent-space diffusion models such as Stable Diffusion.

mindone.diffusers.UniPCMultistepScheduler

Bases: SchedulerMixin, ConfigMixin

UniPCMultistepScheduler is a training-free framework designed for the fast sampling of diffusion models.

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 UniPC order which can be any positive integer. The effective order of accuracy is solver_order + 1 due to the UniC. It is recommended to use solver_order=2 for guided sampling, and solver_order=3 for unconditional sampling. TYPE: `int`, default `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 predict_x0=True. TYPE: `float`, defaults to 1.0 DEFAULT: 1.0
predict_x0	Whether to use the updating algorithm on the predicted x0. TYPE: `bool`, defaults to `True` DEFAULT: True
solver_type	Solver type for UniPC. It is recommended to use bh1 for unconditional sampling when steps < 10, and bh2 otherwise. TYPE: `str`, default `bh2` DEFAULT: 'bh2'
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`, default `True` DEFAULT: True
disable_corrector	Decides which step to disable the corrector to mitigate the misalignment between epsilon_theta(x_t, c) and epsilon_theta(x_t^c, c) which can influence convergence for a large guidance scale. Corrector is usually disabled during the first few steps. TYPE: `list`, default `[]` DEFAULT: []
solver_p	Any other scheduler that if specified, the algorithm becomes solver_p + UniC. TYPE: `SchedulerMixin`, default `None` DEFAULT: None
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
use_exponential_sigmas	Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process. TYPE: `bool`, *optional*, defaults to `False` DEFAULT: False
use_beta_sigmas	Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to Beta Sampling is All You Need for more information. TYPE: `bool`, *optional*, defaults to `False` DEFAULT: False
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
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'
rescale_betas_zero_snr	Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to --offset_noise. TYPE: `bool`, defaults to `False` DEFAULT: False

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

class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
    `UniPCMultistepScheduler` is a training-free framework designed for the fast sampling of diffusion models.

    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`, default `2`):
            The UniPC order which can be any positive integer. The effective order of accuracy is `solver_order + 1`
            due to the UniC. 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 `predict_x0=True`.
        predict_x0 (`bool`, defaults to `True`):
            Whether to use the updating algorithm on the predicted x0.
        solver_type (`str`, default `bh2`):
            Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
            otherwise.
        lower_order_final (`bool`, default `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.
        disable_corrector (`list`, default `[]`):
            Decides which step to disable the corrector to mitigate the misalignment between `epsilon_theta(x_t, c)`
            and `epsilon_theta(x_t^c, c)` which can influence convergence for a large guidance scale. Corrector is
            usually disabled during the first few steps.
        solver_p (`SchedulerMixin`, default `None`):
            Any other scheduler that if specified, the algorithm becomes `solver_p + UniC`.
        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}.
        use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
            Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
        use_beta_sigmas (`bool`, *optional*, defaults to `False`):
            Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
            Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
        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.
        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.
        rescale_betas_zero_snr (`bool`, defaults to `False`):
            Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
            dark samples instead of limiting it to samples with medium brightness. Loosely related to
            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
    """

    _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,
        predict_x0: bool = True,
        solver_type: str = "bh2",
        lower_order_final: bool = True,
        disable_corrector: List[int] = [],
        solver_p: SchedulerMixin = None,
        use_karras_sigmas: Optional[bool] = False,
        use_exponential_sigmas: Optional[bool] = False,
        use_beta_sigmas: Optional[bool] = False,
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
        final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
        rescale_betas_zero_snr: bool = False,
    ):
        if self.config.use_beta_sigmas and not is_scipy_available():
            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
            raise ValueError(
                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
            )
        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__}")

        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

        if rescale_betas_zero_snr:
            # Close to 0 without being 0 so first sigma is not inf
            # FP16 smallest positive subnormal works well here
            self.alphas_cumprod[-1] = 2**-24

        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

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

        self.predict_x0 = predict_x0
        # setable values
        self.num_inference_steps = None
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy()
        self.timesteps = ms.Tensor(timesteps)
        self.model_outputs = [None] * solver_order
        self.timestep_list = [None] * solver_order
        self.lower_order_nums = 0
        self.disable_corrector = disable_corrector
        self.solver_p = solver_p
        self.last_sample = None
        self._step_index = None
        self._begin_index = None

    @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

    def set_timesteps(self, num_inference_steps: int):
        """
        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.
        """
        # "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.config.num_train_timesteps - 1, num_inference_steps + 1)
                .round()[::-1][:-1]
                .copy()
                .astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = self.config.num_train_timesteps // (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][:-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.config.num_train_timesteps, 0, -step_ratio).round().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()
        if self.config.use_karras_sigmas:
            log_sigmas = np.log(sigmas)
            sigmas = np.flip(sigmas).copy()
            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()
            if self.config.final_sigmas_type == "sigma_min":
                sigma_last = sigmas[-1]
            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}"
                )
            sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
        elif self.config.use_exponential_sigmas:
            sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
        elif self.config.use_beta_sigmas:
            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            if self.config.final_sigmas_type == "sigma_min":
                sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
                sigma_last = (
                    sigma_last.asnumpy()
                )  # Transform for numpy concatenate where Torch tensor could be concated with numpy array directly
            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}"
                )
            sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)

        self.sigmas = ms.Tensor(sigmas)
        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
        self.last_sample = None
        if self.solver_p:
            self.solver_p.set_timesteps(self.num_inference_steps)

        # add an index counter for schedulers that allow duplicated timesteps
        self._step_index = None
        self._begin_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_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
    def _convert_to_exponential(self, in_sigmas: ms.Tensor, num_inference_steps: int) -> ms.Tensor:
        """Constructs an exponential noise schedule."""

        # 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()

        sigmas = ops.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps).exp()
        return sigmas

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
    def _convert_to_beta(
        self, in_sigmas: ms.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
    ) -> ms.Tensor:
        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""

        # 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()

        sigmas = ms.Tensor(
            [
                sigma_min + (ppf * (sigma_max - sigma_min))
                for ppf in [
                    scipy.stats.beta.ppf(timestep, alpha, beta)
                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
                ]
            ]
        )
        return sigmas

    def convert_model_output(
        self,
        model_output: ms.Tensor,
        *args,
        sample: ms.Tensor = None,
        **kwargs,
    ) -> ms.Tensor:
        r"""
        Convert the model output to the corresponding type the UniPC algorithm needs.

        Args:
            model_output (`ms.Tensor`):
                The direct output from the 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.

        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`",
            )

        sigmas = self.sigmas.to(dtype=sample.dtype)
        sigma = sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)

        if self.predict_x0:
            if self.config.prediction_type == "epsilon":
                x0_pred = (sample - sigma_t * model_output) / alpha_t
            elif self.config.prediction_type == "sample":
                x0_pred = model_output
            elif self.config.prediction_type == "v_prediction":
                x0_pred = alpha_t * sample - sigma_t * 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 UniPCMultistepScheduler."
                )

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

            return x0_pred
        else:
            if self.config.prediction_type == "epsilon":
                return model_output
            elif self.config.prediction_type == "sample":
                epsilon = (sample - alpha_t * model_output) / sigma_t
                return epsilon
            elif self.config.prediction_type == "v_prediction":
                epsilon = alpha_t * model_output + sigma_t * sample
                return epsilon
            else:
                raise ValueError(
                    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                    " `v_prediction` for the UniPCMultistepScheduler."
                )

    def multistep_uni_p_bh_update(
        self,
        model_output: ms.Tensor,
        *args,
        sample: ms.Tensor = None,
        order: int = None,
        **kwargs,
    ) -> ms.Tensor:
        """
        One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.

        Args:
            model_output (`ms.Tensor`):
                The direct output from the learned diffusion model at the current timestep.
            prev_timestep (`int`):
                The previous discrete timestep in the diffusion chain.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.
            order (`int`):
                The order of UniP at this timestep (corresponds to the *p* in UniPC-p).

        Returns:
            `ms.Tensor`:
                The sample tensor at the previous timestep.
        """
        prev_timestep = args[0] if len(args) > 0 else kwargs.pop("prev_timestep", None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError(" missing `sample` as a required keyward argument")
        if order is None:
            if len(args) > 2:
                order = args[2]
            else:
                raise ValueError(" missing `order` as a required keyward argument")
        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`",
            )
        model_output_list = self.model_outputs

        s0 = self.timestep_list[-1]
        m0 = model_output_list[-1]
        x = sample

        if self.solver_p:
            x_t = self.solver_p.step(model_output, s0, x).prev_sample
            return x_t

        sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)

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

        h = lambda_t - lambda_s0

        rks = []
        D1s = []
        for i in range(1, order):
            si = self.step_index - i
            mi = model_output_list[-(i + 1)]
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = ops.log(alpha_si) - ops.log(sigma_si)
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk.item())
            D1s.append((mi - m0) / rk)

        rks.append(1.0)
        rks = ms.Tensor(rks)

        R = []
        b = []

        hh = -h if self.predict_x0 else h
        h_phi_1 = ops.expm1(hh)  # h\phi_1(h) = e^h - 1
        h_phi_k = h_phi_1 / hh - 1

        factorial_i = 1

        if self.config.solver_type == "bh1":
            B_h = hh
        elif self.config.solver_type == "bh2":
            B_h = ops.expm1(hh)
        else:
            raise NotImplementedError()

        for i in range(1, order + 1):
            R.append(ops.pow(rks, i - 1))
            b.append((h_phi_k * factorial_i / B_h).item())
            factorial_i *= i + 1
            h_phi_k = h_phi_k / hh - 1 / factorial_i

        R = ops.stack(R)
        b = ms.Tensor(b)

        if len(D1s) > 0:
            D1s = ops.stack(D1s, axis=1)  # (B, K)
            # for order 2, we use a simplified version
            if order == 2:
                rhos_p = ms.tensor([0.5], dtype=x.dtype)
            else:
                rhos_p = ms.Tensor(np.linalg.solve(R[:-1, :-1].asnumpy(), b[:-1].asnumpy()), dtype=x.dtype)
        else:
            D1s = None

        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
                pred_res = (rhos_p[:, None] * D1s).sum(axis=1)
            else:
                pred_res = 0
            x_t = x_t_ - alpha_t * B_h * pred_res
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
                pred_res = (rhos_p[:, None] * D1s).sum(axis=1)
            else:
                pred_res = 0
            x_t = x_t_ - sigma_t * B_h * pred_res

        x_t = x_t.to(x.dtype)
        return x_t

    def multistep_uni_c_bh_update(
        self,
        this_model_output: ms.Tensor,
        *args,
        last_sample: ms.Tensor = None,
        this_sample: ms.Tensor = None,
        order: int = None,
        **kwargs,
    ) -> ms.Tensor:
        """
        One step for the UniC (B(h) version).

        Args:
            this_model_output (`ms.Tensor`):
                The model outputs at `x_t`.
            this_timestep (`int`):
                The current timestep `t`.
            last_sample (`ms.Tensor`):
                The generated sample before the last predictor `x_{t-1}`.
            this_sample (`ms.Tensor`):
                The generated sample after the last predictor `x_{t}`.
            order (`int`):
                The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.

        Returns:
            `ms.Tensor`:
                The corrected sample tensor at the current timestep.
        """
        this_timestep = args[0] if len(args) > 0 else kwargs.pop("this_timestep", None)
        if last_sample is None:
            if len(args) > 1:
                last_sample = args[1]
            else:
                raise ValueError(" missing`last_sample` as a required keyward argument")
        if this_sample is None:
            if len(args) > 2:
                this_sample = args[2]
            else:
                raise ValueError(" missing`this_sample` as a required keyward argument")
        if order is None:
            if len(args) > 3:
                order = args[3]
            else:
                raise ValueError(" missing`order` as a required keyward argument")
        if this_timestep is not None:
            deprecate(
                "this_timestep",
                "1.0.0",
                "Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
            )

        model_output_list = self.model_outputs

        m0 = model_output_list[-1]
        x = last_sample
        x_t = this_sample
        model_t = this_model_output

        sigma_t, sigma_s0 = 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)

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

        h = lambda_t - lambda_s0

        rks = []
        D1s = []
        for i in range(1, order):
            si = self.step_index - (i + 1)
            mi = model_output_list[-(i + 1)]
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = ops.log(alpha_si) - ops.log(sigma_si)
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk.item())
            D1s.append((mi - m0) / rk)

        rks.append(1.0)
        rks = ms.Tensor(rks)

        R = []
        b = []

        hh = -h if self.predict_x0 else h
        h_phi_1 = ops.expm1(hh)  # h\phi_1(h) = e^h - 1
        h_phi_k = h_phi_1 / hh - 1

        factorial_i = 1

        if self.config.solver_type == "bh1":
            B_h = hh
        elif self.config.solver_type == "bh2":
            B_h = ops.expm1(hh)
        else:
            raise NotImplementedError()

        for i in range(1, order + 1):
            R.append(ops.pow(rks, i - 1))
            b.append((h_phi_k * factorial_i / B_h).item())
            factorial_i *= i + 1
            h_phi_k = h_phi_k / hh - 1 / factorial_i

        R = ops.stack(R)
        b = ms.Tensor(b)

        if len(D1s) > 0:
            D1s = ops.stack(D1s, axis=1)
        else:
            D1s = None

        # for order 1, we use a simplified version
        if order == 1:
            rhos_c = ms.tensor([0.5], dtype=x.dtype)
        else:
            rhos_c = ms.Tensor(np.linalg.solve(R.asnumpy(), b.asnumpy()), dtype=x.dtype)

        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
                corr_res = (rhos_c[:-1][:, None] * D1s).sum(axis=1)
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
                corr_res = (rhos_c[:-1][:, None] * D1s).sum(axis=1)
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        x_t = x_t.to(x.dtype)
        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: Union[int, ms.Tensor],
        sample: ms.Tensor,
        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 UniPC.

        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.
            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)

        use_corrector = (
            self.step_index > 0 and self.step_index - 1 not in self.disable_corrector and self.last_sample is not None
        )

        model_output_convert = self.convert_model_output(model_output, sample=sample)
        if use_corrector:
            sample = self.multistep_uni_c_bh_update(
                this_model_output=model_output_convert,
                last_sample=self.last_sample,
                this_sample=sample,
                order=self.this_order,
            )

        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
            self.timestep_list[i] = self.timestep_list[i + 1]

        self.model_outputs[-1] = model_output_convert
        self.timestep_list[-1] = timestep

        if self.config.lower_order_final:
            this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
        else:
            this_order = self.config.solver_order

        self.this_order = min(this_order, self.lower_order_nums + 1)  # warmup for multistep
        assert self.this_order > 0

        self.last_sample = sample
        prev_sample = self.multistep_uni_p_bh_update(
            model_output=model_output,  # pass the original non-converted model output, in case solver-p is used
            sample=sample,
            order=self.this_order,
        )

        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)

    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

    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.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.to(dtype=ms.float32)

        # begin_index is None when the 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 before first denoising step to create initial 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))

        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.UniPCMultistepScheduler.begin_index property

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

mindone.diffusers.UniPCMultistepScheduler.step_index property

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

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

Convert the model output to the corresponding type the UniPC algorithm needs.

PARAMETER	DESCRIPTION
model_output	The direct output from the 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` DEFAULT: None

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

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

def convert_model_output(
    self,
    model_output: ms.Tensor,
    *args,
    sample: ms.Tensor = None,
    **kwargs,
) -> ms.Tensor:
    r"""
    Convert the model output to the corresponding type the UniPC algorithm needs.

    Args:
        model_output (`ms.Tensor`):
            The direct output from the 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.

    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`",
        )

    sigmas = self.sigmas.to(dtype=sample.dtype)
    sigma = sigmas[self.step_index]
    alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)

    if self.predict_x0:
        if self.config.prediction_type == "epsilon":
            x0_pred = (sample - sigma_t * model_output) / alpha_t
        elif self.config.prediction_type == "sample":
            x0_pred = model_output
        elif self.config.prediction_type == "v_prediction":
            x0_pred = alpha_t * sample - sigma_t * 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 UniPCMultistepScheduler."
            )

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

        return x0_pred
    else:
        if self.config.prediction_type == "epsilon":
            return model_output
        elif self.config.prediction_type == "sample":
            epsilon = (sample - alpha_t * model_output) / sigma_t
            return epsilon
        elif self.config.prediction_type == "v_prediction":
            epsilon = alpha_t * model_output + sigma_t * sample
            return epsilon
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                " `v_prediction` for the UniPCMultistepScheduler."
            )

mindone.diffusers.UniPCMultistepScheduler.multistep_uni_c_bh_update(this_model_output, *args, last_sample=None, this_sample=None, order=None, **kwargs)

One step for the UniC (B(h) version).

PARAMETER	DESCRIPTION
this_model_output	The model outputs at x_t. TYPE: `ms.Tensor`
this_timestep	The current timestep t. TYPE: `int`
last_sample	The generated sample before the last predictor x_{t-1}. TYPE: `ms.Tensor` DEFAULT: None
this_sample	The generated sample after the last predictor x_{t}. TYPE: `ms.Tensor` DEFAULT: None
order	The p of UniC-p at this step. The effective order of accuracy should be order + 1. TYPE: `int` DEFAULT: None

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

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

def multistep_uni_c_bh_update(
    self,
    this_model_output: ms.Tensor,
    *args,
    last_sample: ms.Tensor = None,
    this_sample: ms.Tensor = None,
    order: int = None,
    **kwargs,
) -> ms.Tensor:
    """
    One step for the UniC (B(h) version).

    Args:
        this_model_output (`ms.Tensor`):
            The model outputs at `x_t`.
        this_timestep (`int`):
            The current timestep `t`.
        last_sample (`ms.Tensor`):
            The generated sample before the last predictor `x_{t-1}`.
        this_sample (`ms.Tensor`):
            The generated sample after the last predictor `x_{t}`.
        order (`int`):
            The `p` of UniC-p at this step. The effective order of accuracy should be `order + 1`.

    Returns:
        `ms.Tensor`:
            The corrected sample tensor at the current timestep.
    """
    this_timestep = args[0] if len(args) > 0 else kwargs.pop("this_timestep", None)
    if last_sample is None:
        if len(args) > 1:
            last_sample = args[1]
        else:
            raise ValueError(" missing`last_sample` as a required keyward argument")
    if this_sample is None:
        if len(args) > 2:
            this_sample = args[2]
        else:
            raise ValueError(" missing`this_sample` as a required keyward argument")
    if order is None:
        if len(args) > 3:
            order = args[3]
        else:
            raise ValueError(" missing`order` as a required keyward argument")
    if this_timestep is not None:
        deprecate(
            "this_timestep",
            "1.0.0",
            "Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
        )

    model_output_list = self.model_outputs

    m0 = model_output_list[-1]
    x = last_sample
    x_t = this_sample
    model_t = this_model_output

    sigma_t, sigma_s0 = 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)

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

    h = lambda_t - lambda_s0

    rks = []
    D1s = []
    for i in range(1, order):
        si = self.step_index - (i + 1)
        mi = model_output_list[-(i + 1)]
        alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
        lambda_si = ops.log(alpha_si) - ops.log(sigma_si)
        rk = (lambda_si - lambda_s0) / h
        rks.append(rk.item())
        D1s.append((mi - m0) / rk)

    rks.append(1.0)
    rks = ms.Tensor(rks)

    R = []
    b = []

    hh = -h if self.predict_x0 else h
    h_phi_1 = ops.expm1(hh)  # h\phi_1(h) = e^h - 1
    h_phi_k = h_phi_1 / hh - 1

    factorial_i = 1

    if self.config.solver_type == "bh1":
        B_h = hh
    elif self.config.solver_type == "bh2":
        B_h = ops.expm1(hh)
    else:
        raise NotImplementedError()

    for i in range(1, order + 1):
        R.append(ops.pow(rks, i - 1))
        b.append((h_phi_k * factorial_i / B_h).item())
        factorial_i *= i + 1
        h_phi_k = h_phi_k / hh - 1 / factorial_i

    R = ops.stack(R)
    b = ms.Tensor(b)

    if len(D1s) > 0:
        D1s = ops.stack(D1s, axis=1)
    else:
        D1s = None

    # for order 1, we use a simplified version
    if order == 1:
        rhos_c = ms.tensor([0.5], dtype=x.dtype)
    else:
        rhos_c = ms.Tensor(np.linalg.solve(R.asnumpy(), b.asnumpy()), dtype=x.dtype)

    if self.predict_x0:
        x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
        if D1s is not None:
            corr_res = (rhos_c[:-1][:, None] * D1s).sum(axis=1)
        else:
            corr_res = 0
        D1_t = model_t - m0
        x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
    else:
        x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
        if D1s is not None:
            corr_res = (rhos_c[:-1][:, None] * D1s).sum(axis=1)
        else:
            corr_res = 0
        D1_t = model_t - m0
        x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
    x_t = x_t.to(x.dtype)
    return x_t

mindone.diffusers.UniPCMultistepScheduler.multistep_uni_p_bh_update(model_output, *args, sample=None, order=None, **kwargs)

One step for the UniP (B(h) version). Alternatively, self.solver_p is used if is specified.

PARAMETER	DESCRIPTION
model_output	The direct output from the learned diffusion model at the current timestep. TYPE: `ms.Tensor`
prev_timestep	The previous discrete timestep in the diffusion chain. TYPE: `int`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor` DEFAULT: None
order	The order of UniP at this timestep (corresponds to the p in UniPC-p). TYPE: `int` DEFAULT: None

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

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

def multistep_uni_p_bh_update(
    self,
    model_output: ms.Tensor,
    *args,
    sample: ms.Tensor = None,
    order: int = None,
    **kwargs,
) -> ms.Tensor:
    """
    One step for the UniP (B(h) version). Alternatively, `self.solver_p` is used if is specified.

    Args:
        model_output (`ms.Tensor`):
            The direct output from the learned diffusion model at the current timestep.
        prev_timestep (`int`):
            The previous discrete timestep in the diffusion chain.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.
        order (`int`):
            The order of UniP at this timestep (corresponds to the *p* in UniPC-p).

    Returns:
        `ms.Tensor`:
            The sample tensor at the previous timestep.
    """
    prev_timestep = args[0] if len(args) > 0 else kwargs.pop("prev_timestep", None)
    if sample is None:
        if len(args) > 1:
            sample = args[1]
        else:
            raise ValueError(" missing `sample` as a required keyward argument")
    if order is None:
        if len(args) > 2:
            order = args[2]
        else:
            raise ValueError(" missing `order` as a required keyward argument")
    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`",
        )
    model_output_list = self.model_outputs

    s0 = self.timestep_list[-1]
    m0 = model_output_list[-1]
    x = sample

    if self.solver_p:
        x_t = self.solver_p.step(model_output, s0, x).prev_sample
        return x_t

    sigma_t, sigma_s0 = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
    alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
    alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)

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

    h = lambda_t - lambda_s0

    rks = []
    D1s = []
    for i in range(1, order):
        si = self.step_index - i
        mi = model_output_list[-(i + 1)]
        alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
        lambda_si = ops.log(alpha_si) - ops.log(sigma_si)
        rk = (lambda_si - lambda_s0) / h
        rks.append(rk.item())
        D1s.append((mi - m0) / rk)

    rks.append(1.0)
    rks = ms.Tensor(rks)

    R = []
    b = []

    hh = -h if self.predict_x0 else h
    h_phi_1 = ops.expm1(hh)  # h\phi_1(h) = e^h - 1
    h_phi_k = h_phi_1 / hh - 1

    factorial_i = 1

    if self.config.solver_type == "bh1":
        B_h = hh
    elif self.config.solver_type == "bh2":
        B_h = ops.expm1(hh)
    else:
        raise NotImplementedError()

    for i in range(1, order + 1):
        R.append(ops.pow(rks, i - 1))
        b.append((h_phi_k * factorial_i / B_h).item())
        factorial_i *= i + 1
        h_phi_k = h_phi_k / hh - 1 / factorial_i

    R = ops.stack(R)
    b = ms.Tensor(b)

    if len(D1s) > 0:
        D1s = ops.stack(D1s, axis=1)  # (B, K)
        # for order 2, we use a simplified version
        if order == 2:
            rhos_p = ms.tensor([0.5], dtype=x.dtype)
        else:
            rhos_p = ms.Tensor(np.linalg.solve(R[:-1, :-1].asnumpy(), b[:-1].asnumpy()), dtype=x.dtype)
    else:
        D1s = None

    if self.predict_x0:
        x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
        if D1s is not None:
            pred_res = (rhos_p[:, None] * D1s).sum(axis=1)
        else:
            pred_res = 0
        x_t = x_t_ - alpha_t * B_h * pred_res
    else:
        x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
        if D1s is not None:
            pred_res = (rhos_p[:, None] * D1s).sum(axis=1)
        else:
            pred_res = 0
        x_t = x_t_ - sigma_t * B_h * pred_res

    x_t = x_t.to(x.dtype)
    return x_t

mindone.diffusers.UniPCMultistepScheduler.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_unipc_multistep.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.UniPCMultistepScheduler.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_unipc_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.UniPCMultistepScheduler.set_timesteps(num_inference_steps)

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`

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

def set_timesteps(self, num_inference_steps: int):
    """
    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.
    """
    # "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.config.num_train_timesteps - 1, num_inference_steps + 1)
            .round()[::-1][:-1]
            .copy()
            .astype(np.int64)
        )
    elif self.config.timestep_spacing == "leading":
        step_ratio = self.config.num_train_timesteps // (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][:-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.config.num_train_timesteps, 0, -step_ratio).round().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()
    if self.config.use_karras_sigmas:
        log_sigmas = np.log(sigmas)
        sigmas = np.flip(sigmas).copy()
        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()
        if self.config.final_sigmas_type == "sigma_min":
            sigma_last = sigmas[-1]
        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}"
            )
        sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
    elif self.config.use_exponential_sigmas:
        sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
        timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
    elif self.config.use_beta_sigmas:
        sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
        timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
    else:
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        if self.config.final_sigmas_type == "sigma_min":
            sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
            sigma_last = (
                sigma_last.asnumpy()
            )  # Transform for numpy concatenate where Torch tensor could be concated with numpy array directly
        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}"
            )
        sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)

    self.sigmas = ms.Tensor(sigmas)
    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
    self.last_sample = None
    if self.solver_p:
        self.solver_p.set_timesteps(self.num_inference_steps)

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

mindone.diffusers.UniPCMultistepScheduler.step(model_output, timestep, sample, return_dict=False)

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

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`
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_unipc_multistep.py

def step(
    self,
    model_output: ms.Tensor,
    timestep: Union[int, ms.Tensor],
    sample: ms.Tensor,
    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 UniPC.

    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.
        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)

    use_corrector = (
        self.step_index > 0 and self.step_index - 1 not in self.disable_corrector and self.last_sample is not None
    )

    model_output_convert = self.convert_model_output(model_output, sample=sample)
    if use_corrector:
        sample = self.multistep_uni_c_bh_update(
            this_model_output=model_output_convert,
            last_sample=self.last_sample,
            this_sample=sample,
            order=self.this_order,
        )

    for i in range(self.config.solver_order - 1):
        self.model_outputs[i] = self.model_outputs[i + 1]
        self.timestep_list[i] = self.timestep_list[i + 1]

    self.model_outputs[-1] = model_output_convert
    self.timestep_list[-1] = timestep

    if self.config.lower_order_final:
        this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
    else:
        this_order = self.config.solver_order

    self.this_order = min(this_order, self.lower_order_nums + 1)  # warmup for multistep
    assert self.this_order > 0

    self.last_sample = sample
    prev_sample = self.multistep_uni_p_bh_update(
        model_output=model_output,  # pass the original non-converted model output, in case solver-p is used
        sample=sample,
        order=self.this_order,
    )

    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)