Add UFOGenScheduler to Community Examples (#6650)

* Add UFOGenScheduler with diffusers imports changed from relative to absolute.

* make style

* Add community README entry for UFOGenScheduler.

examples/community/README.md

@@ -62,6 +62,7 @@ If a community doesn't work as expected, please open an issue and ping the autho
 | AnimateDiff Image-To-Video Pipeline | Experimental Image-To-Video support for AnimateDiff (open to improvements) | [AnimateDiff Image To Video Pipeline](#animatediff-image-to-video-pipeline) | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://drive.google.com/file/d/1TvzCDPHhfFtdcJZe4RLloAwyoLKuttWK/view?usp=sharing) | [Aryan V S](https://github.com/a-r-r-o-w) |
 |   IP Adapter FaceID Stable Diffusion                                                                                               | Stable Diffusion Pipeline that supports IP Adapter Face ID                                                                                                                                                                                                                                                                                                                                                  |  [IP Adapter Face ID](#ip-adapter-face-id) | - | [Fabio Rigano](https://github.com/fabiorigano) |
 |   InstantID Pipeline                                                                                               | Stable Diffusion XL Pipeline that supports InstantID                                                                                                                                                                                                                                                                                                                                                 |  [InstantID Pipeline](#instantid-pipeline) | [![Hugging Face Space](https://img.shields.io/badge/🤗%20Hugging%20Face-Space-yellow)](https://huggingface.co/spaces/InstantX/InstantID) | [Haofan Wang](https://github.com/haofanwang) |
+|   UFOGen Scheduler                                                                                               | Scheduler for UFOGen Model (compatible with Stable Diffusion pipelines)                                                                                                                                                                                                                                                                                                                                                 |  [UFOGen Scheduler](#ufogen-scheduler) | - | [dg845](https://github.com/dg845) |
 
 To load a custom pipeline you just need to pass the `custom_pipeline` argument to `DiffusionPipeline`, as one of the files in `diffusers/examples/community`. Feel free to send a PR with your own pipelines, we will merge them quickly.
 
@@ -3605,3 +3606,32 @@ image = pipe(
     controlnet_conditioning_scale=0.8,
 ).images[0]
 ```
+
+### UFOGen Scheduler
+
+[UFOGen](https://arxiv.org/abs/2311.09257) is a generative model designed for fast one-step text-to-image generation, trained via adversarial training starting from an initial pretrained diffusion model such as Stable Diffusion. `scheduling_ufogen.py` implements a onestep and multistep sampling algorithm for UFOGen models compatible with pipelines like `StableDiffusionPipeline`. A usage example is as follows:
+
+```py
+import torch
+from diffusers import StableDiffusionPipeline
+
+from scheduling_ufogen import UFOGenScheduler
+
+# NOTE: currently, I am not aware of any publicly available UFOGen model checkpoints trained from SD v1.5.
+ufogen_model_id_or_path = "/path/to/ufogen/model"
+pipe = StableDiffusionPipeline(
+    ufogen_model_id_or_path,
+    torch_dtype=torch.float16,
+)
+
+# You can initialize a UFOGenScheduler as follows:
+pipe.scheduler = UFOGenScheduler.from_config(pipe.scheduler.config)
+
+prompt = "Three cats having dinner at a table at new years eve, cinematic shot, 8k."
+
+# Onestep sampling
+onestep_image = pipe(prompt, num_inference_steps=1).images[0]
+
+# Multistep sampling
+multistep_image = pipe(prompt, num_inference_steps=4).images[0]
+```

examples/community/scheduling_ufogen.py

+# Copyright 2023 UC Berkeley Team 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.
+
+# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
+
+import math
+from dataclasses import dataclass
+from typing import List, Optional, Tuple, Union
+
+import numpy as np
+import torch
+
+from diffusers.configuration_utils import ConfigMixin, register_to_config
+from diffusers.schedulers.scheduling_utils import SchedulerMixin
+from diffusers.utils import BaseOutput
+from diffusers.utils.torch_utils import randn_tensor
+
+
+@dataclass
+# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UFOGen
+class UFOGenSchedulerOutput(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.
+        pred_original_sample (`torch.FloatTensor` 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: torch.FloatTensor
+    pred_original_sample: Optional[torch.FloatTensor] = None
+
+
+# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
+def betas_for_alpha_bar(
+    num_diffusion_timesteps,
+    max_beta=0.999,
+    alpha_transform_type="cosine",
+):
+    """
+    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
+    (1-beta) over time from t = [0,1].
+
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
+                     prevent singularities.
+        alpha_transform_type (`str`, *optional*, default to `cosine`): the type of noise schedule for alpha_bar.
+                     Choose from `cosine` or `exp`
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
+    """
+    if alpha_transform_type == "cosine":
+
+        def alpha_bar_fn(t):
+            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    elif alpha_transform_type == "exp":
+
+        def alpha_bar_fn(t):
+            return math.exp(t * -12.0)
+
+    else:
+        raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}")
+
+    betas = []
+    for i in range(num_diffusion_timesteps):
+        t1 = i / num_diffusion_timesteps
+        t2 = (i + 1) / num_diffusion_timesteps
+        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
+    return torch.tensor(betas, dtype=torch.float32)
+
+
+# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
+def rescale_zero_terminal_snr(betas):
+    """
+    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
+
+
+    Args:
+        betas (`torch.FloatTensor`):
+            the betas that the scheduler is being initialized with.
+
+    Returns:
+        `torch.FloatTensor`: rescaled betas with zero terminal SNR
+    """
+    # Convert betas to alphas_bar_sqrt
+    alphas = 1.0 - betas
+    alphas_cumprod = torch.cumprod(alphas, dim=0)
+    alphas_bar_sqrt = alphas_cumprod.sqrt()
+
+    # Store old values.
+    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
+    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
+
+    # Shift so the last timestep is zero.
+    alphas_bar_sqrt -= alphas_bar_sqrt_T
+
+    # Scale so the first timestep is back to the old value.
+    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
+
+    # Convert alphas_bar_sqrt to betas
+    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
+    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
+    alphas = torch.cat([alphas_bar[0:1], alphas])
+    betas = 1 - alphas
+
+    return betas
+
+
+class UFOGenScheduler(SchedulerMixin, ConfigMixin):
+    """
+    `UFOGenScheduler` implements multistep and onestep sampling for a UFOGen model, introduced in
+    [UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANs](https://arxiv.org/abs/2311.09257)
+    by Yanwu Xu, Yang Zhao, Zhisheng Xiao, and Tingbo Hou. UFOGen is a varianet of the denoising diffusion GAN (DDGAN)
+    model designed for one-step sampling.
+
+    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
+    methods the library implements for all schedulers such as loading and saving.
+
+    Args:
+        num_train_timesteps (`int`, defaults to 1000):
+            The number of diffusion steps to train the model.
+        beta_start (`float`, defaults to 0.0001):
+            The starting `beta` value of inference.
+        beta_end (`float`, defaults to 0.02):
+            The final `beta` value.
+        beta_schedule (`str`, defaults to `"linear"`):
+            The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        clip_sample (`bool`, defaults to `True`):
+            Clip the predicted sample for numerical stability.
+        clip_sample_range (`float`, defaults to 1.0):
+            The maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        set_alpha_to_one (`bool`, defaults to `True`):
+            Each diffusion step uses the alphas product value at that step and at the previous one. For the final step
+            there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
+            otherwise it uses the alpha value at step 0.
+        prediction_type (`str`, defaults to `epsilon`, *optional*):
+            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
+            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+            Video](https://imagen.research.google/video/paper.pdf) paper).
+        thresholding (`bool`, defaults to `False`):
+            Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
+            as Stable Diffusion.
+        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+            The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
+        sample_max_value (`float`, defaults to 1.0):
+            The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+        timestep_spacing (`str`, defaults to `"leading"`):
+            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. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False` to make the last step use step 0 for the previous alpha product like in Stable
+            Diffusion.
+        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).
+        denoising_step_size (`int`, defaults to 250):
+            The denoising step size parameter from the UFOGen paper. The number of steps used for training is roughly
+            `math.ceil(num_train_timesteps / denoising_step_size)`.
+    """
+
+    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,
+        clip_sample: bool = True,
+        set_alpha_to_one: bool = True,
+        prediction_type: str = "epsilon",
+        thresholding: bool = False,
+        dynamic_thresholding_ratio: float = 0.995,
+        clip_sample_range: float = 1.0,
+        sample_max_value: float = 1.0,
+        timestep_spacing: str = "leading",
+        steps_offset: int = 0,
+        rescale_betas_zero_snr: bool = False,
+        denoising_step_size: int = 250,
+    ):
+        if trained_betas is not None:
+            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
+        elif beta_schedule == "linear":
+            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
+        elif beta_schedule == "scaled_linear":
+            # this schedule is very specific to the latent diffusion model.
+            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
+        elif beta_schedule == "squaredcos_cap_v2":
+            # Glide cosine schedule
+            self.betas = betas_for_alpha_bar(num_train_timesteps)
+        elif beta_schedule == "sigmoid":
+            # GeoDiff sigmoid schedule
+            betas = torch.linspace(-6, 6, num_train_timesteps)
+            self.betas = torch.sigmoid(betas) * (beta_end - beta_start) + beta_start
+        else:
+            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
+
+        # Rescale for zero SNR
+        if rescale_betas_zero_snr:
+            self.betas = rescale_zero_terminal_snr(self.betas)
+
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
+
+        # For the final step, there is no previous alphas_cumprod because we are already at 0
+        # `set_alpha_to_one` decides whether we set this parameter simply to one or
+        # whether we use the final alpha of the "non-previous" one.
+        self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
+
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
+        # setable values
+        self.custom_timesteps = False
+        self.num_inference_steps = None
+        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())
+
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`):
+                The input sample.
+            timestep (`int`, *optional*):
+                The current timestep in the diffusion chain.
+
+        Returns:
+            `torch.FloatTensor`:
+                A scaled input sample.
+        """
+        return sample
+
+    def set_timesteps(
+        self,
+        num_inference_steps: Optional[int] = None,
+        device: Union[str, torch.device] = None,
+        timesteps: Optional[List[int]] = 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. If used,
+                `timesteps` must be `None`.
+            device (`str` or `torch.device`, *optional*):
+                The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            timesteps (`List[int]`, *optional*):
+                Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default
+                timestep spacing strategy of equal spacing between timesteps is used. If `timesteps` is passed,
+                `num_inference_steps` must be `None`.
+
+        """
+        if num_inference_steps is not None and timesteps is not None:
+            raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.")
+
+        if timesteps is not None:
+            for i in range(1, len(timesteps)):
+                if timesteps[i] >= timesteps[i - 1]:
+                    raise ValueError("`custom_timesteps` must be in descending order.")
+
+            if timesteps[0] >= self.config.num_train_timesteps:
+                raise ValueError(
+                    f"`timesteps` must start before `self.config.train_timesteps`:"
+                    f" {self.config.num_train_timesteps}."
+                )
+
+            timesteps = np.array(timesteps, dtype=np.int64)
+            self.custom_timesteps = True
+        else:
+            if num_inference_steps > self.config.num_train_timesteps:
+                raise ValueError(
+                    f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
+                    f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
+                    f" maximal {self.config.num_train_timesteps} timesteps."
+                )
+
+            self.num_inference_steps = num_inference_steps
+            self.custom_timesteps = False
+
+            # TODO: For now, handle special case when num_inference_steps == 1 separately
+            if num_inference_steps == 1:
+                # Set the timestep schedule to num_train_timesteps - 1 rather than 0
+                # (that is, the one-step timestep schedule is always trailing rather than leading or linspace)
+                timesteps = np.array([self.config.num_train_timesteps - 1], dtype=np.int64)
+            else:
+                # TODO: For now, retain the DDPM timestep spacing logic
+                # "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)
+                        .round()[::-1]
+                        .copy()
+                        .astype(np.int64)
+                    )
+                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.int64)
+                    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.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64)
+                    timesteps -= 1
+                else:
+                    raise ValueError(
+                        f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."
+                    )
+
+        self.timesteps = torch.from_numpy(timesteps).to(device)
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
+    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
+        """
+        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
+        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
+        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
+        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
+        photorealism as well as better image-text alignment, especially when using very large guidance weights."
+
+        https://arxiv.org/abs/2205.11487
+        """
+        dtype = sample.dtype
+        batch_size, channels, *remaining_dims = sample.shape
+
+        if dtype not in (torch.float32, torch.float64):
+            sample = sample.float()  # upcast for quantile calculation, and clamp not implemented for cpu half
+
+        # Flatten sample for doing quantile calculation along each image
+        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
+
+        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"
+
+        s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
+        s = torch.clamp(
+            s, min=1, max=self.config.sample_max_value
+        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
+        s = s.unsqueeze(1)  # (batch_size, 1) because clamp will broadcast along dim=0
+        sample = torch.clamp(sample, -s, s) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"
+
+        sample = sample.reshape(batch_size, channels, *remaining_dims)
+        sample = sample.to(dtype)
+
+        return sample
+
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        generator: Optional[torch.Generator] = None,
+        return_dict: bool = True,
+    ) -> Union[UFOGenSchedulerOutput, 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`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_ufogen.UFOGenSchedulerOutput`] or `tuple`.
+
+        Returns:
+            [`~schedulers.scheduling_ddpm.UFOGenSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_ufogen.UFOGenSchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
+
+        """
+        # 0. Resolve timesteps
+        t = timestep
+        prev_t = self.previous_timestep(t)
+
+        # 1. compute alphas, betas
+        alpha_prod_t = self.alphas_cumprod[t]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.final_alpha_cumprod
+        beta_prod_t = 1 - alpha_prod_t
+        # beta_prod_t_prev = 1 - alpha_prod_t_prev
+        # current_alpha_t = alpha_prod_t / alpha_prod_t_prev
+        # current_beta_t = 1 - current_alpha_t
+
+        # 2. compute predicted original sample from predicted noise also called
+        # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
+        if self.config.prediction_type == "epsilon":
+            pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
+        elif self.config.prediction_type == "sample":
+            pred_original_sample = model_output
+        elif self.config.prediction_type == "v_prediction":
+            pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
+        else:
+            raise ValueError(
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"
+                " `v_prediction`  for UFOGenScheduler."
+            )
+
+        # 3. Clip or threshold "predicted x_0"
+        if self.config.thresholding:
+            pred_original_sample = self._threshold_sample(pred_original_sample)
+        elif self.config.clip_sample:
+            pred_original_sample = pred_original_sample.clamp(
+                -self.config.clip_sample_range, self.config.clip_sample_range
+            )
+
+        # 4. Single-step or multi-step sampling
+        # Noise is not used on the final timestep of the timestep schedule.
+        # This also means that noise is not used for one-step sampling.
+        if t != self.timesteps[-1]:
+            # TODO: is this correct?
+            # Sample prev sample x_{t - 1} ~ q(x_{t - 1} | x_0 =  G(x_t, t))
+            device = model_output.device
+            noise = randn_tensor(model_output.shape, generator=generator, device=device, dtype=model_output.dtype)
+            sqrt_alpha_prod_t_prev = alpha_prod_t_prev**0.5
+            sqrt_one_minus_alpha_prod_t_prev = (1 - alpha_prod_t_prev) ** 0.5
+            pred_prev_sample = sqrt_alpha_prod_t_prev * pred_original_sample + sqrt_one_minus_alpha_prod_t_prev * noise
+        else:
+            # Simply return the pred_original_sample. If `prediction_type == "sample"`, this is equivalent to returning
+            # the output of the GAN generator U-Net on the initial noisy latents x_T ~ N(0, I).
+            pred_prev_sample = pred_original_sample
+
+        if not return_dict:
+            return (pred_prev_sample,)
+
+        return UFOGenSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample)
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
+    def add_noise(
+        self,
+        original_samples: torch.FloatTensor,
+        noise: torch.FloatTensor,
+        timesteps: torch.IntTensor,
+    ) -> torch.FloatTensor:
+        # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
+        alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
+        timesteps = timesteps.to(original_samples.device)
+
+        sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
+        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
+        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
+            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
+
+        sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
+        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
+        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
+            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)
+
+        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
+        return noisy_samples
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity
+    def get_velocity(
+        self, sample: torch.FloatTensor, noise: torch.FloatTensor, timesteps: torch.IntTensor
+    ) -> torch.FloatTensor:
+        # Make sure alphas_cumprod and timestep have same device and dtype as sample
+        alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
+        timesteps = timesteps.to(sample.device)
+
+        sqrt_alpha_prod = alphas_cumprod[timesteps] ** 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[timesteps]) ** 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
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.previous_timestep
+    def previous_timestep(self, timestep):
+        if self.custom_timesteps:
+            index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0]
+            if index == self.timesteps.shape[0] - 1:
+                prev_t = torch.tensor(-1)
+            else:
+                prev_t = self.timesteps[index + 1]
+        else:
+            num_inference_steps = (
+                self.num_inference_steps if self.num_inference_steps else self.config.num_train_timesteps
+            )
+            prev_t = timestep - self.config.num_train_timesteps // num_inference_steps
+
+        return prev_t