flow matching lcm scheduler (#11170)

* add flow matching lcm scheduler
* stochastic sampling
* upscaling for scale-wise generation

* Apply style fixes

* Apply suggestions from code review
Co-authored-by: hlky <hlky@hlky.ac>

---------
Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: YiYi Xu <yixu310@gmail.com>
Co-authored-by: hlky <hlky@hlky.ac>

src/diffusers/schedulers/scheduling_flow_match_lcm.py

+# Copyright 2024 Stability AI, Katherine Crowson and The HuggingFace Team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import math
+from dataclasses import dataclass
+from typing import List, Optional, Tuple, Union
+
+import numpy as np
+import torch
+
+from ..configuration_utils import ConfigMixin, register_to_config
+from ..utils import BaseOutput, is_scipy_available, logging
+from ..utils.torch_utils import randn_tensor
+from .scheduling_utils import SchedulerMixin
+
+
+if is_scipy_available():
+    import scipy.stats
+
+logger = logging.get_logger(__name__)  # pylint: disable=invalid-name
+
+
+@dataclass
+class FlowMatchLCMSchedulerOutput(BaseOutput):
+    """
+    Output class for the scheduler's `step` function output.
+
+    Args:
+        prev_sample (`torch.FloatTensor` 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.
+    """
+
+    prev_sample: torch.FloatTensor
+
+
+class FlowMatchLCMScheduler(SchedulerMixin, ConfigMixin):
+    """
+    LCM scheduler for Flow Matching.
+
+    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.
+        shift (`float`, defaults to 1.0):
+            The shift value for the timestep schedule.
+        use_dynamic_shifting (`bool`, defaults to False):
+            Whether to apply timestep shifting on-the-fly based on the image resolution.
+        base_shift (`float`, defaults to 0.5):
+            Value to stabilize image generation. Increasing `base_shift` reduces variation and image is more consistent
+            with desired output.
+        max_shift (`float`, defaults to 1.15):
+            Value change allowed to latent vectors. Increasing `max_shift` encourages more variation and image may be
+            more exaggerated or stylized.
+        base_image_seq_len (`int`, defaults to 256):
+            The base image sequence length.
+        max_image_seq_len (`int`, defaults to 4096):
+            The maximum image sequence length.
+        invert_sigmas (`bool`, defaults to False):
+            Whether to invert the sigmas.
+        shift_terminal (`float`, defaults to None):
+            The end value of the shifted timestep schedule.
+        use_karras_sigmas (`bool`, defaults to False):
+            Whether to use Karras sigmas for step sizes in the noise schedule during sampling.
+        use_exponential_sigmas (`bool`, defaults to False):
+            Whether to use exponential sigmas for step sizes in the noise schedule during sampling.
+        use_beta_sigmas (`bool`, defaults to False):
+            Whether to use beta sigmas for step sizes in the noise schedule during sampling.
+        time_shift_type (`str`, defaults to "exponential"):
+            The type of dynamic resolution-dependent timestep shifting to apply. Either "exponential" or "linear".
+        scale_factors ('list', defaults to None)
+            It defines how to scale the latents at which predictions are made.
+        upscale_mode ('str', defaults to 'bicubic')
+            Upscaling method, applied if scale-wise generation is considered
+    """
+
+    _compatibles = []
+    order = 1
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        shift: float = 1.0,
+        use_dynamic_shifting: bool = False,
+        base_shift: Optional[float] = 0.5,
+        max_shift: Optional[float] = 1.15,
+        base_image_seq_len: Optional[int] = 256,
+        max_image_seq_len: Optional[int] = 4096,
+        invert_sigmas: bool = False,
+        shift_terminal: Optional[float] = None,
+        use_karras_sigmas: Optional[bool] = False,
+        use_exponential_sigmas: Optional[bool] = False,
+        use_beta_sigmas: Optional[bool] = False,
+        time_shift_type: str = "exponential",
+        scale_factors: Optional[List[float]] = None,
+        upscale_mode: Optional[str] = "bicubic",
+    ):
+        if self.config.use_beta_sigmas and not is_scipy_available():
+            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
+        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
+            raise ValueError(
+                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
+            )
+        if time_shift_type not in {"exponential", "linear"}:
+            raise ValueError("`time_shift_type` must either be 'exponential' or 'linear'.")
+
+        timesteps = np.linspace(1, num_train_timesteps, num_train_timesteps, dtype=np.float32)[::-1].copy()
+        timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32)
+
+        sigmas = timesteps / num_train_timesteps
+        if not use_dynamic_shifting:
+            # when use_dynamic_shifting is True, we apply the timestep shifting on the fly based on the image resolution
+            sigmas = shift * sigmas / (1 + (shift - 1) * sigmas)
+
+        self.timesteps = sigmas * num_train_timesteps
+
+        self._step_index = None
+        self._begin_index = None
+
+        self._shift = shift
+
+        self._init_size = None
+        self._scale_factors = scale_factors
+        self._upscale_mode = upscale_mode
+
+        self.sigmas = sigmas.to("cpu")  # to avoid too much CPU/GPU communication
+        self.sigma_min = self.sigmas[-1].item()
+        self.sigma_max = self.sigmas[0].item()
+
+    @property
+    def shift(self):
+        """
+        The value used for shifting.
+        """
+        return self._shift
+
+    @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_shift(self, shift: float):
+        self._shift = shift
+
+    def set_scale_factors(self, scale_factors: list, upscale_mode):
+        """
+        Sets scale factors for a scale-wise generation regime.
+
+        Args:
+            scale_factors (`list`):
+                The scale factors for each step
+            upscale_mode (`str`):
+                Upscaling method
+        """
+        self._scale_factors = scale_factors
+        self._upscale_mode = upscale_mode
+
+    def scale_noise(
+        self,
+        sample: torch.FloatTensor,
+        timestep: Union[float, torch.FloatTensor],
+        noise: Optional[torch.FloatTensor] = None,
+    ) -> torch.FloatTensor:
+        """
+        Forward process in flow-matching
+
+        Args:
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
+
+        Returns:
+            `torch.FloatTensor`:
+                A scaled input sample.
+        """
+        # Make sure sigmas and timesteps have the same device and dtype as original_samples
+        sigmas = self.sigmas.to(device=sample.device, dtype=sample.dtype)
+
+        if sample.device.type == "mps" and torch.is_floating_point(timestep):
+            # mps does not support float64
+            schedule_timesteps = self.timesteps.to(sample.device, dtype=torch.float32)
+            timestep = timestep.to(sample.device, dtype=torch.float32)
+        else:
+            schedule_timesteps = self.timesteps.to(sample.device)
+            timestep = timestep.to(sample.device)
+
+        # 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 timestep]
+        elif self.step_index is not None:
+            # add_noise is called after first denoising step (for inpainting)
+            step_indices = [self.step_index] * timestep.shape[0]
+        else:
+            # add noise is called before first denoising step to create initial latent(img2img)
+            step_indices = [self.begin_index] * timestep.shape[0]
+
+        sigma = sigmas[step_indices].flatten()
+        while len(sigma.shape) < len(sample.shape):
+            sigma = sigma.unsqueeze(-1)
+
+        sample = sigma * noise + (1.0 - sigma) * sample
+
+        return sample
+
+    def _sigma_to_t(self, sigma):
+        return sigma * self.config.num_train_timesteps
+
+    def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
+        if self.config.time_shift_type == "exponential":
+            return self._time_shift_exponential(mu, sigma, t)
+        elif self.config.time_shift_type == "linear":
+            return self._time_shift_linear(mu, sigma, t)
+
+    def stretch_shift_to_terminal(self, t: torch.Tensor) -> torch.Tensor:
+        r"""
+        Stretches and shifts the timestep schedule to ensure it terminates at the configured `shift_terminal` config
+        value.
+
+        Reference:
+        https://github.com/Lightricks/LTX-Video/blob/a01a171f8fe3d99dce2728d60a73fecf4d4238ae/ltx_video/schedulers/rf.py#L51
+
+        Args:
+            t (`torch.Tensor`):
+                A tensor of timesteps to be stretched and shifted.
+
+        Returns:
+            `torch.Tensor`:
+                A tensor of adjusted timesteps such that the final value equals `self.config.shift_terminal`.
+        """
+        one_minus_z = 1 - t
+        scale_factor = one_minus_z[-1] / (1 - self.config.shift_terminal)
+        stretched_t = 1 - (one_minus_z / scale_factor)
+        return stretched_t
+
+    def set_timesteps(
+        self,
+        num_inference_steps: Optional[int] = None,
+        device: Union[str, torch.device] = None,
+        sigmas: Optional[List[float]] = None,
+        mu: Optional[float] = None,
+        timesteps: Optional[List[float]] = None,
+    ):
+        """
+        Sets the discrete timesteps used for the diffusion chain (to be run before inference).
+
+        Args:
+            num_inference_steps (`int`, *optional*):
+                The number of diffusion steps used when generating samples with a pre-trained model.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            sigmas (`List[float]`, *optional*):
+                Custom values for sigmas to be used for each diffusion step. If `None`, the sigmas are computed
+                automatically.
+            mu (`float`, *optional*):
+                Determines the amount of shifting applied to sigmas when performing resolution-dependent timestep
+                shifting.
+            timesteps (`List[float]`, *optional*):
+                Custom values for timesteps to be used for each diffusion step. If `None`, the timesteps are computed
+                automatically.
+        """
+        if self.config.use_dynamic_shifting and mu is None:
+            raise ValueError("`mu` must be passed when `use_dynamic_shifting` is set to be `True`")
+
+        if sigmas is not None and timesteps is not None:
+            if len(sigmas) != len(timesteps):
+                raise ValueError("`sigmas` and `timesteps` should have the same length")
+
+        if num_inference_steps is not None:
+            if (sigmas is not None and len(sigmas) != num_inference_steps) or (
+                timesteps is not None and len(timesteps) != num_inference_steps
+            ):
+                raise ValueError(
+                    "`sigmas` and `timesteps` should have the same length as num_inference_steps, if `num_inference_steps` is provided"
+                )
+        else:
+            num_inference_steps = len(sigmas) if sigmas is not None else len(timesteps)
+
+        self.num_inference_steps = num_inference_steps
+
+        # 1. Prepare default sigmas
+        is_timesteps_provided = timesteps is not None
+
+        if is_timesteps_provided:
+            timesteps = np.array(timesteps).astype(np.float32)
+
+        if sigmas is None:
+            if timesteps is None:
+                timesteps = np.linspace(
+                    self._sigma_to_t(self.sigma_max), self._sigma_to_t(self.sigma_min), num_inference_steps
+                )
+            sigmas = timesteps / self.config.num_train_timesteps
+        else:
+            sigmas = np.array(sigmas).astype(np.float32)
+            num_inference_steps = len(sigmas)
+
+        # 2. Perform timestep shifting. Either no shifting is applied, or resolution-dependent shifting of
+        #    "exponential" or "linear" type is applied
+        if self.config.use_dynamic_shifting:
+            sigmas = self.time_shift(mu, 1.0, sigmas)
+        else:
+            sigmas = self.shift * sigmas / (1 + (self.shift - 1) * sigmas)
+
+        # 3. If required, stretch the sigmas schedule to terminate at the configured `shift_terminal` value
+        if self.config.shift_terminal:
+            sigmas = self.stretch_shift_to_terminal(sigmas)
+
+        # 4. If required, convert sigmas to one of karras, exponential, or beta sigma schedules
+        if self.config.use_karras_sigmas:
+            sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
+        elif self.config.use_exponential_sigmas:
+            sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
+        elif self.config.use_beta_sigmas:
+            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
+
+        # 5. Convert sigmas and timesteps to tensors and move to specified device
+        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32, device=device)
+        if not is_timesteps_provided:
+            timesteps = sigmas * self.config.num_train_timesteps
+        else:
+            timesteps = torch.from_numpy(timesteps).to(dtype=torch.float32, device=device)
+
+        # 6. Append the terminal sigma value.
+        #    If a model requires inverted sigma schedule for denoising but timesteps without inversion, the
+        #    `invert_sigmas` flag can be set to `True`. This case is only required in Mochi
+        if self.config.invert_sigmas:
+            sigmas = 1.0 - sigmas
+            timesteps = sigmas * self.config.num_train_timesteps
+            sigmas = torch.cat([sigmas, torch.ones(1, device=sigmas.device)])
+        else:
+            sigmas = torch.cat([sigmas, torch.zeros(1, device=sigmas.device)])
+
+        self.timesteps = timesteps
+        self.sigmas = sigmas
+        self._step_index = None
+        self._begin_index = None
+
+    def index_for_timestep(self, timestep, schedule_timesteps=None):
+        if schedule_timesteps is None:
+            schedule_timesteps = self.timesteps
+
+        indices = (schedule_timesteps == timestep).nonzero()
+
+        # 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)
+        pos = 1 if len(indices) > 1 else 0
+
+        return indices[pos].item()
+
+    def _init_step_index(self, timestep):
+        if self.begin_index is None:
+            if isinstance(timestep, torch.Tensor):
+                timestep = timestep.to(self.timesteps.device)
+            self._step_index = self.index_for_timestep(timestep)
+        else:
+            self._step_index = self._begin_index
+
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: Union[float, torch.FloatTensor],
+        sample: torch.FloatTensor,
+        generator: Optional[torch.Generator] = None,
+        return_dict: bool = True,
+    ) -> Union[FlowMatchLCMSchedulerOutput, 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 (`torch.FloatTensor`):
+                The direct output from learned diffusion model.
+            timestep (`float`):
+                The current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                A current instance of a sample created by the diffusion process.
+            generator (`torch.Generator`, *optional*):
+                A random number generator.
+            return_dict (`bool`):
+                Whether or not to return a [`~schedulers.scheduling_flow_match_lcm.FlowMatchLCMSchedulerOutput`] or
+                tuple.
+
+        Returns:
+            [`~schedulers.scheduling_flow_match_lcm.FlowMatchLCMSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_flow_match_lcm.FlowMatchLCMSchedulerOutput`] is
+                returned, otherwise a tuple is returned where the first element is the sample tensor.
+        """
+
+        if (
+            isinstance(timestep, int)
+            or isinstance(timestep, torch.IntTensor)
+            or isinstance(timestep, torch.LongTensor)
+        ):
+            raise ValueError(
+                (
+                    "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
+                    " `FlowMatchLCMScheduler.step()` is not supported. Make sure to pass"
+                    " one of the `scheduler.timesteps` as a timestep."
+                ),
+            )
+
+        if self._scale_factors and self._upscale_mode and len(self.timesteps) != len(self._scale_factors) + 1:
+            raise ValueError(
+                "`_scale_factors` should have the same length as `timesteps` - 1, if `_scale_factors` are set."
+            )
+
+        if self._init_size is None or self.step_index is None:
+            self._init_size = model_output.size()[2:]
+
+        if self.step_index is None:
+            self._init_step_index(timestep)
+
+        # Upcast to avoid precision issues when computing prev_sample
+        sample = sample.to(torch.float32)
+
+        sigma = self.sigmas[self.step_index]
+        sigma_next = self.sigmas[self.step_index + 1]
+        x0_pred = sample - sigma * model_output
+
+        if self._scale_factors and self._upscale_mode:
+            if self._step_index < len(self._scale_factors):
+                size = [round(self._scale_factors[self._step_index] * size) for size in self._init_size]
+                x0_pred = torch.nn.functional.interpolate(x0_pred, size=size, mode=self._upscale_mode)
+
+        noise = randn_tensor(x0_pred.shape, generator=generator, device=x0_pred.device, dtype=x0_pred.dtype)
+        prev_sample = (1 - sigma_next) * x0_pred + sigma_next * noise
+
+        # upon completion increase step index by one
+        self._step_index += 1
+        # Cast sample back to model compatible dtype
+        prev_sample = prev_sample.to(model_output.dtype)
+
+        if not return_dict:
+            return (prev_sample,)
+
+        return FlowMatchLCMSchedulerOutput(prev_sample=prev_sample)
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
+    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
+        """Constructs the noise schedule of Karras et al. (2022)."""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        rho = 7.0  # 7.0 is the value used in the paper
+        ramp = np.linspace(0, 1, num_inference_steps)
+        min_inv_rho = sigma_min ** (1 / rho)
+        max_inv_rho = sigma_max ** (1 / rho)
+        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
+        return sigmas
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
+    def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
+        """Constructs an exponential noise schedule."""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps))
+        return sigmas
+
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
+    def _convert_to_beta(
+        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
+    ) -> torch.Tensor:
+        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = np.array(
+            [
+                sigma_min + (ppf * (sigma_max - sigma_min))
+                for ppf in [
+                    scipy.stats.beta.ppf(timestep, alpha, beta)
+                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
+                ]
+            ]
+        )
+        return sigmas
+
+    def _time_shift_exponential(self, mu, sigma, t):
+        return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)
+
+    def _time_shift_linear(self, mu, sigma, t):
+        return mu / (mu + (1 / t - 1) ** sigma)
+
+    def __len__(self):
+        return self.config.num_train_timesteps