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DEISMultistepScheduler

Diffusion Exponential Integrator Sampler (DEIS) is proposed in Fast Sampling of Diffusion Models with Exponential Integrator by Qinsheng Zhang and Yongxin Chen. DEISMultistepScheduler is a fast high order solver for diffusion ordinary differential equations (ODEs).

This implementation modifies the polynomial fitting formula in log-rho space instead of the original linear t space in the DEIS paper. The modification enjoys closed-form coefficients for exponential multistep update instead of replying on the numerical solver.

The abstract from the paper is:

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at this https URL.

Tips

It is recommended to set solver_order to 2 or 3, while solver_order=1 is equivalent to DDIMScheduler.

Dynamic thresholding from Imagen is supported, and for pixel-space diffusion models, you can set thresholding=True to use the dynamic thresholding.

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler

Bases: SchedulerMixin, ConfigMixin

DEISMultistepScheduler is a fast high order solver for diffusion ordinary differential equations (ODEs).

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 DEIS 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` 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.

TYPE: `float`, defaults to 1.0 DEFAULT: 1.0

algorithm_type

The algorithm type for the solver.

TYPE: `str`, defaults to `deis` DEFAULT: 'deis'

lower_order_final

Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.

TYPE: `bool`, defaults to `True` DEFAULT: True

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

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_deis_multistep.py
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class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
    """
    `DEISMultistepScheduler` is a fast high order solver for diffusion ordinary differential equations (ODEs).

    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 DEIS 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`):
            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`.
        algorithm_type (`str`, defaults to `deis`):
            The algorithm type for the solver.
        lower_order_final (`bool`, defaults to `True`):
            Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
        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}.
        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[np.ndarray] = 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 = "deis",
        solver_type: str = "logrho",
        lower_order_final: bool = True,
        use_karras_sigmas: Optional[bool] = False,
        timestep_spacing: str = "linspace",
        steps_offset: int = 0,
    ):
        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 DEIS
        if algorithm_type not in ["deis"]:
            if algorithm_type in ["dpmsolver", "dpmsolver++"]:
                self.register_to_config(algorithm_type="deis")
            else:
                raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}")

        if solver_type not in ["logrho"]:
            if solver_type in ["midpoint", "heun", "bh1", "bh2"]:
                self.register_to_config(solver_type="logrho")
            else:
                raise NotImplementedError(f"solver type {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)[::-1].copy()
        self.timesteps = ms.Tensor(timesteps)
        self.model_outputs = [None] * solver_order
        self.lower_order_nums = 0
        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()
            sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
        else:
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
            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

        # 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

    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 DEIS 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`",
            )

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

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

        if self.config.algorithm_type == "deis":
            return (sample - alpha_t * x0_pred) / sigma_t
        else:
            raise NotImplementedError("only support log-rho multistep deis now")

    def deis_first_order_update(
        self,
        model_output: ms.Tensor,
        *args,
        sample: ms.Tensor = None,
        **kwargs,
    ) -> ms.Tensor:
        """
        One step for the first-order DEIS (equivalent to DDIM).

        Args:
            model_output (`ms.Tensor`):
                The direct output from the learned diffusion model.
            timestep (`int`):
                The current discrete timestep in the diffusion chain.
            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.

        Returns:
            `ms.Tensor`:
                The sample tensor at the previous timestep.
        """
        timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
        dtype = sample.dtype
        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 == "deis":
            x_t = (alpha_t / alpha_s).to(dtype) * sample - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * model_output
        else:
            raise NotImplementedError("only support log-rho multistep deis now")
        return x_t

    def multistep_deis_second_order_update(
        self,
        model_output_list: List[ms.Tensor],
        *args,
        sample: ms.Tensor = None,
        **kwargs,
    ) -> ms.Tensor:
        """
        One step for the second-order multistep DEIS.

        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.
        """
        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        dtype = sample.dtype
        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)

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

        rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1

        if self.config.algorithm_type == "deis":

            def ind_fn(t, b, c):
                # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
                return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))

            coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
            coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)

            x_t = alpha_t.to(dtype) * (sample / alpha_s0.to(dtype) + coef1.to(dtype) * m0 + coef2.to(dtype) * m1)
            return x_t
        else:
            raise NotImplementedError("only support log-rho multistep deis now")

    def multistep_deis_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 DEIS.

        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.
        """

        timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
        dtype = sample.dtype
        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)

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

        rho_t, rho_s0, rho_s1, rho_s2 = (
            sigma_t / alpha_t,
            sigma_s0 / alpha_s0,
            sigma_s1 / alpha_s1,
            sigma_s2 / alpha_s2,
        )

        if self.config.algorithm_type == "deis":

            def ind_fn(t, b, c, d):
                # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
                numerator = t * (
                    np.log(c) * (np.log(d) - np.log(t) + 1)
                    - np.log(d) * np.log(t)
                    + np.log(d)
                    + np.log(t) ** 2
                    - 2 * np.log(t)
                    + 2
                )
                denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
                return numerator / denominator

            coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
            coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
            coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)

            x_t = alpha_t.to(dtype) * (
                sample / alpha_s0.to(dtype) + coef1.to(dtype) * m0 + coef2.to(dtype) * m1 + coef3.to(dtype) * m2
            )

            return x_t
        else:
            raise NotImplementedError("only support log-rho multistep deis now")

    # 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 DEIS.

        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)

        lower_order_final = (
            (self.step_index == len(self.timesteps) - 1) and 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.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
            prev_sample = self.deis_first_order_update(model_output, sample=sample)
        elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
            prev_sample = self.multistep_deis_second_order_update(self.model_outputs, sample=sample)
        else:
            prev_sample = self.multistep_deis_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)

    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:
        # Make sure sigmas and timesteps have the same device and dtype as original_samples
        broadcast_shape = original_samples.shape
        sigmas = self.sigmas.to(dtype=original_samples.dtype)
        schedule_timesteps = self.timesteps

        # 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.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.begin_index property

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

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.step_index property

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

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.convert_model_output(model_output, *args, sample=None, **kwargs)

Convert the model output to the corresponding type the DEIS 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_deis_multistep.py
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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 DEIS 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`",
        )

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

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

    if self.config.algorithm_type == "deis":
        return (sample - alpha_t * x0_pred) / sigma_t
    else:
        raise NotImplementedError("only support log-rho multistep deis now")

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.deis_first_order_update(model_output, *args, sample=None, **kwargs)

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

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`

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

RETURNS DESCRIPTION
Tensor

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

Source code in mindone/diffusers/schedulers/scheduling_deis_multistep.py
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def deis_first_order_update(
    self,
    model_output: ms.Tensor,
    *args,
    sample: ms.Tensor = None,
    **kwargs,
) -> ms.Tensor:
    """
    One step for the first-order DEIS (equivalent to DDIM).

    Args:
        model_output (`ms.Tensor`):
            The direct output from the learned diffusion model.
        timestep (`int`):
            The current discrete timestep in the diffusion chain.
        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.

    Returns:
        `ms.Tensor`:
            The sample tensor at the previous timestep.
    """
    timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None)
    dtype = sample.dtype
    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 == "deis":
        x_t = (alpha_t / alpha_s).to(dtype) * sample - (sigma_t * (ops.exp(h) - 1.0)).to(dtype) * model_output
    else:
        raise NotImplementedError("only support log-rho multistep deis now")
    return x_t

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.multistep_deis_second_order_update(model_output_list, *args, sample=None, **kwargs)

One step for the second-order multistep DEIS.

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_deis_multistep.py
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def multistep_deis_second_order_update(
    self,
    model_output_list: List[ms.Tensor],
    *args,
    sample: ms.Tensor = None,
    **kwargs,
) -> ms.Tensor:
    """
    One step for the second-order multistep DEIS.

    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.
    """
    timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
    dtype = sample.dtype
    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)

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

    rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1

    if self.config.algorithm_type == "deis":

        def ind_fn(t, b, c):
            # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
            return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))

        coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
        coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)

        x_t = alpha_t.to(dtype) * (sample / alpha_s0.to(dtype) + coef1.to(dtype) * m0 + coef2.to(dtype) * m1)
        return x_t
    else:
        raise NotImplementedError("only support log-rho multistep deis now")

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.multistep_deis_third_order_update(model_output_list, *args, sample=None, **kwargs)

One step for the third-order multistep DEIS.

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_deis_multistep.py
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def multistep_deis_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 DEIS.

    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.
    """

    timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None)
    dtype = sample.dtype
    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)

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

    rho_t, rho_s0, rho_s1, rho_s2 = (
        sigma_t / alpha_t,
        sigma_s0 / alpha_s0,
        sigma_s1 / alpha_s1,
        sigma_s2 / alpha_s2,
    )

    if self.config.algorithm_type == "deis":

        def ind_fn(t, b, c, d):
            # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}]
            numerator = t * (
                np.log(c) * (np.log(d) - np.log(t) + 1)
                - np.log(d) * np.log(t)
                + np.log(d)
                + np.log(t) ** 2
                - 2 * np.log(t)
                + 2
            )
            denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
            return numerator / denominator

        coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
        coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
        coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)

        x_t = alpha_t.to(dtype) * (
            sample / alpha_s0.to(dtype) + coef1.to(dtype) * m0 + coef2.to(dtype) * m1 + coef3.to(dtype) * m2
        )

        return x_t
    else:
        raise NotImplementedError("only support log-rho multistep deis now")

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.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_deis_multistep.py
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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.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.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_deis_multistep.py
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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.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.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_deis_multistep.py
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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()
        sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32)
    else:
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
        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

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

mindone.diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler.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 DEIS.

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_deis_multistep.py
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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 DEIS.

    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)

    lower_order_final = (
        (self.step_index == len(self.timesteps) - 1) and 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.solver_order == 1 or self.lower_order_nums < 1 or lower_order_final:
        prev_sample = self.deis_first_order_update(model_output, sample=sample)
    elif self.config.solver_order == 2 or self.lower_order_nums < 2 or lower_order_second:
        prev_sample = self.multistep_deis_second_order_update(self.model_outputs, sample=sample)
    else:
        prev_sample = self.multistep_deis_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)