LMSDiscreteScheduler

LMSDiscreteScheduler is a linear multistep scheduler for discrete beta schedules. The scheduler is ported from and created by Katherine Crowson, and the original implementation can be found at crowsonkb/k-diffusion.

mindone.diffusers.LMSDiscreteScheduler

Bases: SchedulerMixin, ConfigMixin

A linear multistep scheduler for discrete beta schedules.

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 or scaled_linear. 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
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
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'
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_lms_discrete.py

class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
    A linear multistep scheduler for discrete beta schedules.

    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` or `scaled_linear`.
        trained_betas (`np.ndarray`, *optional*):
            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
        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}.
        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).
        timestep_spacing (`str`, defaults to `"linspace"`):
            The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
            Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
        steps_offset (`int`, defaults to 0):
            An offset added to the inference steps, as required by some model families.
    """

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

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        use_karras_sigmas: Optional[bool] = False,
        prediction_type: str = "epsilon",
        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)

        sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).asnumpy()
        sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32)
        self.sigmas = ms.Tensor(sigmas)

        # setable values
        self.num_inference_steps = None
        self.use_karras_sigmas = use_karras_sigmas
        self.set_timesteps(num_train_timesteps)
        self.derivatives = []
        self.is_scale_input_called = False

        self._step_index = None
        self._begin_index = None

    @property
    def init_noise_sigma(self):
        # standard deviation of the initial noise distribution
        if self.config.timestep_spacing in ["linspace", "trailing"]:
            return self.sigmas.max()

        return (self.sigmas.max() ** 2 + 1) ** 0.5

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

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

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

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

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

        Args:
            sample (`ms.Tensor`):
                The input sample.
            timestep (`float` or `ms.Tensor`):
                The current timestep in the diffusion chain.

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

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

        sigma = self.sigmas[self.step_index]
        sample = (sample / ((sigma**2 + 1) ** 0.5)).to(sample.dtype)
        self.is_scale_input_called = True
        return sample

    def get_lms_coefficient(self, order, t, current_order):
        """
        Compute the linear multistep coefficient.

        Args:
            order ():
            t ():
            current_order ():
        """

        def lms_derivative(tau):
            prod = 1.0
            for k in range(order):
                if current_order == k:
                    continue
                prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
            return prod

        integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0]

        return integrated_coeff

    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.
        """
        self.num_inference_steps = num_inference_steps

        # "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, dtype=np.float32)[
                ::-1
            ].copy()
        elif self.config.timestep_spacing == "leading":
            step_ratio = self.config.num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.float32)
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / self.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.float32)
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
            )

        sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).asnumpy()
        log_sigmas = np.log(sigmas)
        sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)

        if self.config.use_karras_sigmas:
            sigmas = self._convert_to_karras(in_sigmas=sigmas)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).astype(np.float32)

        sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)

        self.sigmas = ms.Tensor(sigmas)
        self.timesteps = ms.Tensor(timesteps)
        self._step_index = None
        self._begin_index = None

        self.derivatives = []

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

        if (schedule_timesteps == timestep).sum() > 1:
            pos = 1
        else:
            pos = 0

        # 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)
        indices = (schedule_timesteps == timestep).nonzero()

        return int(indices[pos])

    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
    def _init_step_index(self, timestep):
        if self.begin_index is None:
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index

    # 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_euler_discrete.EulerDiscreteScheduler._convert_to_karras
    def _convert_to_karras(self, in_sigmas: ms.Tensor) -> ms.Tensor:
        """Constructs the noise schedule of Karras et al. (2022)."""

        sigma_min: float = in_sigmas[-1].item()
        sigma_max: float = in_sigmas[0].item()

        rho = 7.0  # 7.0 is the value used in the paper
        ramp = np.linspace(0, 1, self.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 step(
        self,
        model_output: ms.Tensor,
        timestep: Union[float, ms.Tensor],
        sample: ms.Tensor,
        order: int = 4,
        return_dict: bool = False,
    ) -> Union[LMSDiscreteSchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`ms.Tensor`):
                The direct output from learned diffusion model.
            timestep (`float` or `ms.Tensor`):
                The current discrete timestep in the diffusion chain.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.
            order (`int`, defaults to 4):
                The order of the linear multistep method.
            return_dict (`bool`, *optional*, defaults to `False`):
                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 not self.is_scale_input_called:
            warnings.warn(
                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                "See `StableDiffusionPipeline` for a usage example."
            )

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

        sigma = self.sigmas[self.step_index]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        if self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma.to(model_output.dtype) * model_output
        elif self.config.prediction_type == "v_prediction":
            # * c_out + input * c_skip
            pred_original_sample = (model_output * (-sigma / (sigma**2 + 1) ** 0.5)).to(model_output.dtype) + (
                sample / (sigma**2 + 1)
            ).to(sample.dtype)
        elif self.config.prediction_type == "sample":
            pred_original_sample = model_output
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
            )

        # 2. Convert to an ODE derivative
        derivative = ((sample - pred_original_sample) / sigma).to(sample.dtype)
        self.derivatives.append(derivative)
        if len(self.derivatives) > order:
            self.derivatives.pop(0)

        # 3. Compute linear multistep coefficients
        order = min(self.step_index + 1, order)
        lms_coeffs = [self.get_lms_coefficient(order, self.step_index, curr_order) for curr_order in range(order)]

        # 4. Compute previous sample based on the derivatives path
        prev_sample = sample + sum(
            (ms.tensor(coeff) * derivative).to(derivative.dtype)
            for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives))
        )

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

        if not return_dict:
            return (prev_sample,)

        return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

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

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

        noisy_samples = original_samples + noise * sigma
        return noisy_samples

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

mindone.diffusers.LMSDiscreteScheduler.begin_index property

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

mindone.diffusers.LMSDiscreteScheduler.step_index property

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

mindone.diffusers.LMSDiscreteScheduler.get_lms_coefficient(order, t, current_order)

Compute the linear multistep coefficient.

PARAMETER	DESCRIPTION
order
t
current_order

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

def get_lms_coefficient(self, order, t, current_order):
    """
    Compute the linear multistep coefficient.

    Args:
        order ():
        t ():
        current_order ():
    """

    def lms_derivative(tau):
        prod = 1.0
        for k in range(order):
            if current_order == k:
                continue
            prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
        return prod

    integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0]

    return integrated_coeff

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

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`
timestep	The current timestep in the diffusion chain. TYPE: `float` or `ms.Tensor`

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

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

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

    Args:
        sample (`ms.Tensor`):
            The input sample.
        timestep (`float` or `ms.Tensor`):
            The current timestep in the diffusion chain.

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

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

    sigma = self.sigmas[self.step_index]
    sample = (sample / ((sigma**2 + 1) ** 0.5)).to(sample.dtype)
    self.is_scale_input_called = True
    return sample

mindone.diffusers.LMSDiscreteScheduler.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_lms_discrete.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.LMSDiscreteScheduler.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_lms_discrete.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.
    """
    self.num_inference_steps = num_inference_steps

    # "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, dtype=np.float32)[
            ::-1
        ].copy()
    elif self.config.timestep_spacing == "leading":
        step_ratio = self.config.num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.float32)
        timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
        step_ratio = self.config.num_train_timesteps / self.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.float32)
        timesteps -= 1
    else:
        raise ValueError(
            f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
        )

    sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).asnumpy()
    log_sigmas = np.log(sigmas)
    sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)

    if self.config.use_karras_sigmas:
        sigmas = self._convert_to_karras(in_sigmas=sigmas)
        timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).astype(np.float32)

    sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)

    self.sigmas = ms.Tensor(sigmas)
    self.timesteps = ms.Tensor(timesteps)
    self._step_index = None
    self._begin_index = None

    self.derivatives = []

mindone.diffusers.LMSDiscreteScheduler.step(model_output, timestep, sample, order=4, return_dict=False)

Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion process from the learned model outputs (most often the predicted noise).

PARAMETER	DESCRIPTION
model_output	The direct output from learned diffusion model. TYPE: `ms.Tensor`
timestep	The current discrete timestep in the diffusion chain. TYPE: `float` or `ms.Tensor`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor`
order	The order of the linear multistep method. TYPE: `int`, defaults to 4 DEFAULT: 4
return_dict	Whether or not to return a [~schedulers.scheduling_utils.SchedulerOutput] or tuple. TYPE: `bool`, *optional*, defaults to `False` DEFAULT: False

RETURNS	DESCRIPTION
Union[LMSDiscreteSchedulerOutput, 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_lms_discrete.py

def step(
    self,
    model_output: ms.Tensor,
    timestep: Union[float, ms.Tensor],
    sample: ms.Tensor,
    order: int = 4,
    return_dict: bool = False,
) -> Union[LMSDiscreteSchedulerOutput, Tuple]:
    """
    Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
    process from the learned model outputs (most often the predicted noise).

    Args:
        model_output (`ms.Tensor`):
            The direct output from learned diffusion model.
        timestep (`float` or `ms.Tensor`):
            The current discrete timestep in the diffusion chain.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.
        order (`int`, defaults to 4):
            The order of the linear multistep method.
        return_dict (`bool`, *optional*, defaults to `False`):
            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 not self.is_scale_input_called:
        warnings.warn(
            "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
            "See `StableDiffusionPipeline` for a usage example."
        )

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

    sigma = self.sigmas[self.step_index]

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
        pred_original_sample = sample - sigma.to(model_output.dtype) * model_output
    elif self.config.prediction_type == "v_prediction":
        # * c_out + input * c_skip
        pred_original_sample = (model_output * (-sigma / (sigma**2 + 1) ** 0.5)).to(model_output.dtype) + (
            sample / (sigma**2 + 1)
        ).to(sample.dtype)
    elif self.config.prediction_type == "sample":
        pred_original_sample = model_output
    else:
        raise ValueError(
            f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
        )

    # 2. Convert to an ODE derivative
    derivative = ((sample - pred_original_sample) / sigma).to(sample.dtype)
    self.derivatives.append(derivative)
    if len(self.derivatives) > order:
        self.derivatives.pop(0)

    # 3. Compute linear multistep coefficients
    order = min(self.step_index + 1, order)
    lms_coeffs = [self.get_lms_coefficient(order, self.step_index, curr_order) for curr_order in range(order)]

    # 4. Compute previous sample based on the derivatives path
    prev_sample = sample + sum(
        (ms.tensor(coeff) * derivative).to(derivative.dtype)
        for coeff, derivative in zip(lms_coeffs, reversed(self.derivatives))
    )

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

    if not return_dict:
        return (prev_sample,)

    return LMSDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

mindone.diffusers.schedulers.scheduling_lms_discrete.LMSDiscreteSchedulerOutput dataclass

Bases: BaseOutput

Output class for the scheduler's step function output.

PARAMETER	DESCRIPTION
prev_sample	Computed sample (x_{t-1}) of previous timestep. prev_sample should be used as next model input in the denoising loop. TYPE: `ms.Tensor` of shape `(batch_size, num_channels, height, width)` for images
pred_original_sample	The predicted denoised sample (x_{0}) based on the model output from the current timestep. pred_original_sample can be used to preview progress or for guidance. TYPE: `ms.Tensor` of shape `(batch_size, num_channels, height, width)` for images DEFAULT: None

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

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class LMSDiscreteSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's `step` function output.

    Args:
        prev_sample (`ms.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
        pred_original_sample (`ms.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
            `pred_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: ms.Tensor
    pred_original_sample: Optional[ms.Tensor] = None