EulerDiscreteScheduler

The Euler scheduler (Algorithm 2) is from the Elucidating the Design Space of Diffusion-Based Generative Models paper by Karras et al. This is a fast scheduler which can often generate good outputs in 20-30 steps. The scheduler is based on the original k-diffusion implementation by Katherine Crowson.

mindone.diffusers.EulerDiscreteScheduler

Bases: SchedulerMixin, ConfigMixin

Euler scheduler.

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
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'
interpolation_type(`str`,	The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of "linear" or "log_linear". TYPE: defaults to `"linear"`, *optional*
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
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
final_sigmas_type	The final sigma value for the noise schedule during the sampling process. If "sigma_min", the final sigma is the same as the last sigma in the training schedule. If zero, the final sigma is set to 0. TYPE: `str`, defaults to `"zero"` DEFAULT: 'zero'

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

class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
    """
    Euler scheduler.

    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`.
        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).
        interpolation_type(`str`, defaults to `"linear"`, *optional*):
            The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of
            `"linear"` or `"log_linear"`.
        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.
        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).
        final_sigmas_type (`str`, defaults to `"zero"`):
            The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
            sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
    """

    _compatibles = [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,
        prediction_type: str = "epsilon",
        interpolation_type: str = "linear",
        use_karras_sigmas: Optional[bool] = False,
        sigma_min: Optional[float] = None,
        sigma_max: Optional[float] = None,
        timestep_spacing: str = "linspace",
        timestep_type: str = "discrete",  # can be "discrete" or "continuous"
        steps_offset: int = 0,
        rescale_betas_zero_snr: bool = False,
        final_sigmas_type: str = "zero",  # can be "zero" or "sigma_min"
    ):
        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)

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = ops.cumprod(self.alphas, dim=0)

        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

        sigmas = (((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5).flip((0,))
        timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
        timesteps = ms.Tensor(timesteps).to(dtype=ms.float32)

        # setable values
        self.num_inference_steps = None

        # TODO: Support the full EDM scalings for all prediction types and timestep types
        if timestep_type == "continuous" and prediction_type == "v_prediction":
            self.timesteps = ms.Tensor([0.25 * sigma.log().item() for sigma in sigmas])
        else:
            self.timesteps = timesteps

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

        self.is_scale_input_called = False
        self.use_karras_sigmas = use_karras_sigmas

        self._step_index = None
        self._begin_index = None

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

        return (max_sigma**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. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.

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

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

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

        self.is_scale_input_called = True
        return sample

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

        Args:
            num_inference_steps (`int`):
                The number of diffusion steps used when generating samples with a pre-trained model.
            timesteps (`List[int]`, *optional*):
                Custom timesteps used to support arbitrary timesteps schedule. If `None`, timesteps will be generated
                based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` and `sigmas`
                must be `None`, and `timestep_spacing` attribute will be ignored.
            sigmas (`List[float]`, *optional*):
                Custom sigmas used to support arbitrary timesteps schedule schedule. If `None`, timesteps and sigmas
                will be generated based on the relevant scheduler attributes. If `sigmas` is passed,
                `num_inference_steps` and `timesteps` must be `None`, and the timesteps will be generated based on the
                custom sigmas schedule.
        """

        if timesteps is not None and sigmas is not None:
            raise ValueError("Only one of `timesteps` or `sigmas` should be set.")
        if num_inference_steps is None and timesteps is None and sigmas is None:
            raise ValueError("Must pass exactly one of `num_inference_steps` or `timesteps` or `sigmas.")
        if num_inference_steps is not None and (timesteps is not None or sigmas is not None):
            raise ValueError("Can only pass one of `num_inference_steps` or `timesteps` or `sigmas`.")
        if timesteps is not None and self.config.use_karras_sigmas:
            raise ValueError("Cannot set `timesteps` with `config.use_karras_sigmas = True`.")
        if (
            timesteps is not None
            and self.config.timestep_type == "continuous"
            and self.config.prediction_type == "v_prediction"
        ):
            raise ValueError(
                "Cannot set `timesteps` with `config.timestep_type = 'continuous'` and `config.prediction_type = 'v_prediction'`."
            )

        if num_inference_steps is None:
            num_inference_steps = len(timesteps) if timesteps is not None else len(sigmas) - 1
        self.num_inference_steps = num_inference_steps

        if sigmas is not None:
            log_sigmas = np.log(np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5))
            sigmas = np.array(sigmas).astype(np.float32)
            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas[:-1]])

        else:
            if timesteps is not None:
                timesteps = np.array(timesteps).astype(np.float32)
            else:
                # "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)

            if self.config.interpolation_type == "linear":
                sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
            elif self.config.interpolation_type == "log_linear":
                sigmas = np.exp(np.linspace(np.log(sigmas[-1]), np.log(sigmas[0]), num_inference_steps + 1))
            else:
                raise ValueError(
                    f"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
                    " 'linear' or 'log_linear'"
                )

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

        sigmas = ms.Tensor(sigmas).to(dtype=ms.float32)

        # TODO: Support the full EDM scalings for all prediction types and timestep types
        if self.config.timestep_type == "continuous" and self.config.prediction_type == "v_prediction":
            self.timesteps = ms.Tensor([0.25 * sigma.log().item() for sigma in sigmas[:-1]])
        else:
            self.timesteps = ms.Tensor(timesteps.astype(np.float32))

        self._step_index = None
        self._begin_index = None
        self.sigmas = sigmas

    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 https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
    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 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])

    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

    def step(
        self,
        model_output: ms.Tensor,
        timestep: Union[float, ms.Tensor],
        sample: ms.Tensor,
        s_churn: float = 0.0,
        s_tmin: float = 0.0,
        s_tmax: float = float("inf"),
        s_noise: float = 1.0,
        generator: Optional[Union[List["np.random.Generator"], "np.random.Generator"]] = None,
        return_dict: bool = False,
    ) -> Union[EulerDiscreteSchedulerOutput, 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`):
                The current discrete timestep in the diffusion chain.
            sample (`ms.Tensor`):
                A current instance of a sample created by the diffusion process.
            s_churn (`float`):
            s_tmin  (`float`):
            s_tmax  (`float`):
            s_noise (`float`, defaults to 1.0):
                Scaling factor for noise added to the sample.
            generator (`np.random.Generator`, *optional*):
                A random number generator.
            return_dict (`bool`):
                Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
                tuple.

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

        if isinstance(timestep, int) or (isinstance(timestep, ms.Tensor) and timestep.dtype in [ms.int32, ms.int64]):
            raise ValueError(
                (
                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                    " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                    " one of the `scheduler.timesteps` as a timestep."
                ),
            )

        if not self.is_scale_input_called:
            logger.warning(
                "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)

        # Upcast to avoid precision issues when computing prev_sample
        sample = sample.to(ms.float32)

        sigma = self.sigmas[self.step_index]

        gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

        noise = randn_tensor(model_output.shape, dtype=model_output.dtype, generator=generator)

        eps = noise * s_noise
        sigma_hat = sigma * (gamma + 1)

        if gamma > 0:
            sample = sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        # NOTE: "original_sample" should not be an expected prediction_type but is left in for
        # backwards compatibility
        if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
            pred_original_sample = model_output
        elif self.config.prediction_type == "epsilon":
            pred_original_sample = sample - sigma_hat.to(model_output.dtype) * model_output
        elif self.config.prediction_type == "v_prediction":
            # denoised = model_output * c_out + input * c_skip
            pred_original_sample = (model_output * (-sigma / (sigma**2 + 1) ** 0.5)).to(model_output.dtype) + (
                sample / (sigma**2 + 1)
            )
        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_hat

        dt = self.sigmas[self.step_index + 1] - sigma_hat

        prev_sample = sample + derivative * dt

        # Cast sample back to model compatible dtype
        prev_sample = prev_sample.to(model_output.dtype)

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

        if not return_dict:
            return (prev_sample,)

        return EulerDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

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

        # 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]
        else:
            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 get_velocity(self, sample: ms.Tensor, noise: ms.Tensor, timesteps: ms.Tensor) -> ms.Tensor:
        if isinstance(timesteps, int) or (isinstance(timesteps, ms.Tensor) and timesteps.dtype in [ms.int32, ms.int64]):
            raise ValueError(
                (
                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                    " `EulerDiscreteScheduler.get_velocity()` is not supported. Make sure to pass"
                    " one of the `scheduler.timesteps` as a timestep."
                ),
            )

        schedule_timesteps = self.timesteps

        step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
        alphas_cumprod = self.alphas_cumprod.to(sample.dtype)
        sqrt_alpha_prod = alphas_cumprod[step_indices] ** 0.5
        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
        while len(sqrt_alpha_prod.shape) < len(sample.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)

        sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[step_indices]) ** 0.5
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

        velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
        return velocity

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

mindone.diffusers.EulerDiscreteScheduler.begin_index property

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

mindone.diffusers.EulerDiscreteScheduler.step_index property

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

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

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

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

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

Source code in mindone/diffusers/schedulers/scheduling_euler_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. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm.

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

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

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

    self.is_scale_input_called = True
    return sample

mindone.diffusers.EulerDiscreteScheduler.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_euler_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.EulerDiscreteScheduler.set_timesteps(num_inference_steps=None, timesteps=None, sigmas=None)

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

PARAMETER	DESCRIPTION
num_inference_steps	The number of diffusion steps used when generating samples with a pre-trained model. TYPE: `int` DEFAULT: None
timesteps	Custom timesteps used to support arbitrary timesteps schedule. If None, timesteps will be generated based on the timestep_spacing attribute. If timesteps is passed, num_inference_steps and sigmas must be None, and timestep_spacing attribute will be ignored. TYPE: `List[int]`, *optional* DEFAULT: None
sigmas	Custom sigmas used to support arbitrary timesteps schedule schedule. If None, timesteps and sigmas will be generated based on the relevant scheduler attributes. If sigmas is passed, num_inference_steps and timesteps must be None, and the timesteps will be generated based on the custom sigmas schedule. TYPE: `List[float]`, *optional* DEFAULT: None

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

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

    Args:
        num_inference_steps (`int`):
            The number of diffusion steps used when generating samples with a pre-trained model.
        timesteps (`List[int]`, *optional*):
            Custom timesteps used to support arbitrary timesteps schedule. If `None`, timesteps will be generated
            based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` and `sigmas`
            must be `None`, and `timestep_spacing` attribute will be ignored.
        sigmas (`List[float]`, *optional*):
            Custom sigmas used to support arbitrary timesteps schedule schedule. If `None`, timesteps and sigmas
            will be generated based on the relevant scheduler attributes. If `sigmas` is passed,
            `num_inference_steps` and `timesteps` must be `None`, and the timesteps will be generated based on the
            custom sigmas schedule.
    """

    if timesteps is not None and sigmas is not None:
        raise ValueError("Only one of `timesteps` or `sigmas` should be set.")
    if num_inference_steps is None and timesteps is None and sigmas is None:
        raise ValueError("Must pass exactly one of `num_inference_steps` or `timesteps` or `sigmas.")
    if num_inference_steps is not None and (timesteps is not None or sigmas is not None):
        raise ValueError("Can only pass one of `num_inference_steps` or `timesteps` or `sigmas`.")
    if timesteps is not None and self.config.use_karras_sigmas:
        raise ValueError("Cannot set `timesteps` with `config.use_karras_sigmas = True`.")
    if (
        timesteps is not None
        and self.config.timestep_type == "continuous"
        and self.config.prediction_type == "v_prediction"
    ):
        raise ValueError(
            "Cannot set `timesteps` with `config.timestep_type = 'continuous'` and `config.prediction_type = 'v_prediction'`."
        )

    if num_inference_steps is None:
        num_inference_steps = len(timesteps) if timesteps is not None else len(sigmas) - 1
    self.num_inference_steps = num_inference_steps

    if sigmas is not None:
        log_sigmas = np.log(np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5))
        sigmas = np.array(sigmas).astype(np.float32)
        timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas[:-1]])

    else:
        if timesteps is not None:
            timesteps = np.array(timesteps).astype(np.float32)
        else:
            # "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)

        if self.config.interpolation_type == "linear":
            sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
        elif self.config.interpolation_type == "log_linear":
            sigmas = np.exp(np.linspace(np.log(sigmas[-1]), np.log(sigmas[0]), num_inference_steps + 1))
        else:
            raise ValueError(
                f"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
                " 'linear' or 'log_linear'"
            )

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

    sigmas = ms.Tensor(sigmas).to(dtype=ms.float32)

    # TODO: Support the full EDM scalings for all prediction types and timestep types
    if self.config.timestep_type == "continuous" and self.config.prediction_type == "v_prediction":
        self.timesteps = ms.Tensor([0.25 * sigma.log().item() for sigma in sigmas[:-1]])
    else:
        self.timesteps = ms.Tensor(timesteps.astype(np.float32))

    self._step_index = None
    self._begin_index = None
    self.sigmas = sigmas

mindone.diffusers.EulerDiscreteScheduler.step(model_output, timestep, sample, s_churn=0.0, s_tmin=0.0, s_tmax=float('inf'), s_noise=1.0, generator=None, 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`
sample	A current instance of a sample created by the diffusion process. TYPE: `ms.Tensor`
s_churn	TYPE: `float` DEFAULT: 0.0
s_tmin	TYPE: (`float` DEFAULT: 0.0
s_tmax	TYPE: (`float` DEFAULT: float('inf')
s_noise	Scaling factor for noise added to the sample. TYPE: `float`, defaults to 1.0 DEFAULT: 1.0
generator	A random number generator. TYPE: `np.random.Generator`, *optional* DEFAULT: None
return_dict	Whether or not to return a [~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput] or tuple. TYPE: `bool` DEFAULT: False

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

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

def step(
    self,
    model_output: ms.Tensor,
    timestep: Union[float, ms.Tensor],
    sample: ms.Tensor,
    s_churn: float = 0.0,
    s_tmin: float = 0.0,
    s_tmax: float = float("inf"),
    s_noise: float = 1.0,
    generator: Optional[Union[List["np.random.Generator"], "np.random.Generator"]] = None,
    return_dict: bool = False,
) -> Union[EulerDiscreteSchedulerOutput, 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`):
            The current discrete timestep in the diffusion chain.
        sample (`ms.Tensor`):
            A current instance of a sample created by the diffusion process.
        s_churn (`float`):
        s_tmin  (`float`):
        s_tmax  (`float`):
        s_noise (`float`, defaults to 1.0):
            Scaling factor for noise added to the sample.
        generator (`np.random.Generator`, *optional*):
            A random number generator.
        return_dict (`bool`):
            Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
            tuple.

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

    if isinstance(timestep, int) or (isinstance(timestep, ms.Tensor) and timestep.dtype in [ms.int32, ms.int64]):
        raise ValueError(
            (
                "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                " one of the `scheduler.timesteps` as a timestep."
            ),
        )

    if not self.is_scale_input_called:
        logger.warning(
            "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)

    # Upcast to avoid precision issues when computing prev_sample
    sample = sample.to(ms.float32)

    sigma = self.sigmas[self.step_index]

    gamma = min(s_churn / (len(self.sigmas) - 1), 2**0.5 - 1) if s_tmin <= sigma <= s_tmax else 0.0

    noise = randn_tensor(model_output.shape, dtype=model_output.dtype, generator=generator)

    eps = noise * s_noise
    sigma_hat = sigma * (gamma + 1)

    if gamma > 0:
        sample = sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    # NOTE: "original_sample" should not be an expected prediction_type but is left in for
    # backwards compatibility
    if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
        pred_original_sample = model_output
    elif self.config.prediction_type == "epsilon":
        pred_original_sample = sample - sigma_hat.to(model_output.dtype) * model_output
    elif self.config.prediction_type == "v_prediction":
        # denoised = model_output * c_out + input * c_skip
        pred_original_sample = (model_output * (-sigma / (sigma**2 + 1) ** 0.5)).to(model_output.dtype) + (
            sample / (sigma**2 + 1)
        )
    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_hat

    dt = self.sigmas[self.step_index + 1] - sigma_hat

    prev_sample = sample + derivative * dt

    # Cast sample back to model compatible dtype
    prev_sample = prev_sample.to(model_output.dtype)

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

    if not return_dict:
        return (prev_sample,)

    return EulerDiscreteSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

mindone.diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput 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_euler_discrete.py

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class EulerDiscreteSchedulerOutput(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