Create scheduling_ddim.py

scheduling_ddim.py

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+# Copyright 2023 Stanford University 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 code is strongly influenced by https://github.com/pesser/pytorch_diffusion
+# and https://github.com/hojonathanho/diffusion
+
+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, randn_tensor
+from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
+
+
+@dataclass
+# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
+class DDIMSchedulerOutput(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) -> torch.Tensor:
+    """
+    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.
+
+    Returns:
+        betas (`np.ndarray`): the betas used by the scheduler to step the model outputs
+    """
+
+    def alpha_bar(time_step):
+        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    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(t2) / alpha_bar(t1), max_beta))
+    return torch.tensor(betas, dtype=torch.float32)
+
+
+class DDIMScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
+    diffusion probabilistic models (DDPMs) with non-Markovian guidance.
+
+    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
+    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
+    [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
+    [`~SchedulerMixin.from_pretrained`] functions.
+
+    For more details, see the original paper: https://arxiv.org/abs/2010.02502
+
+    Args:
+        num_train_timesteps (`int`): number of diffusion steps used to train the model.
+        beta_start (`float`): the starting `beta` value of inference.
+        beta_end (`float`): the final `beta` value.
+        beta_schedule (`str`):
+            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        trained_betas (`np.ndarray`, optional):
+            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
+        clip_sample (`bool`, default `True`):
+            option to clip predicted sample for numerical stability.
+        clip_sample_range (`float`, default `1.0`):
+            the maximum magnitude for sample clipping. Valid only when `clip_sample=True`.
+        set_alpha_to_one (`bool`, default `True`):
+            each diffusion step uses the value of alphas product 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 value of alpha at step 0.
+        steps_offset (`int`, default `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, as done in
+            stable diffusion.
+        prediction_type (`str`, default `epsilon`, optional):
+            prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
+            process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
+            https://imagen.research.google/video/paper.pdf)
+        thresholding (`bool`, default `False`):
+            whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487).
+            Note that the thresholding method is unsuitable for latent-space diffusion models (such as
+            stable-diffusion).
+        dynamic_thresholding_ratio (`float`, default `0.995`):
+            the ratio for the dynamic thresholding method. Default is `0.995`, the same as Imagen
+            (https://arxiv.org/abs/2205.11487). Valid only when `thresholding=True`.
+        sample_max_value (`float`, default `1.0`):
+            the threshold value for dynamic thresholding. Valid only when `thresholding=True`.
+    """
+
+    _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,
+        clip_sample: bool = True,
+        set_alpha_to_one: bool = True,
+        steps_offset: int = 0,
+        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,
+    ):
+        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)
+        else:
+            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
+
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
+
+        # At every step in ddim, we are looking into the previous alphas_cumprod
+        # 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.num_inference_steps = None
+        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64))
+
+    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`): input sample
+            timestep (`int`, optional): current timestep
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
+    def _get_variance(self, timestep, prev_timestep):
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+        beta_prod_t = 1 - alpha_prod_t
+        beta_prod_t_prev = 1 - alpha_prod_t_prev
+
+        variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
+
+        return variance
+
+    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
+    def _threshold_sample(self, sample: torch.FloatTensor) -> torch.FloatTensor:
+        # Dynamic thresholding in https://arxiv.org/abs/2205.11487
+        dynamic_max_val = (
+            sample.flatten(1)
+            .abs()
+            .quantile(self.config.dynamic_thresholding_ratio, dim=1)
+            .clamp_min(self.config.sample_max_value)
+            .view(-1, *([1] * (sample.ndim - 1)))
+        )
+        return sample.clamp(-dynamic_max_val, dynamic_max_val) / dynamic_max_val
+
+    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
+        """
+        Sets the discrete timesteps used for the diffusion chain. Supporting function 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 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
+        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)
+        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.timesteps += self.config.steps_offset
+
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        eta: float = 0.0,
+        use_clipped_model_output: bool = False,
+        generator=None,
+        variance_noise: Optional[torch.FloatTensor] = None,
+        return_dict: bool = True,
+    ) -> Union[DDIMSchedulerOutput, Tuple]:
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            model_output (`torch.FloatTensor`): direct output from learned diffusion model.
+            timestep (`int`): current discrete timestep in the diffusion chain.
+            sample (`torch.FloatTensor`):
+                current instance of sample being created by diffusion process.
+            eta (`float`): weight of noise for added noise in diffusion step.
+            use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped
+                predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when
+                `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would
+                coincide with the one provided as input and `use_clipped_model_output` will have not effect.
+            generator: random number generator.
+            variance_noise (`torch.FloatTensor`): instead of generating noise for the variance using `generator`, we
+                can directly provide the noise for the variance itself. This is useful for methods such as
+                CycleDiffusion. (https://arxiv.org/abs/2210.05559)
+            return_dict (`bool`): option for returning tuple rather than DDIMSchedulerOutput class
+
+        Returns:
+            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
+            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
+            returning a tuple, the first element is the sample tensor.
+
+        """
+        if self.num_inference_steps is None:
+            raise ValueError(
+                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
+            )
+
+        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
+        # Ideally, read DDIM paper in-detail understanding
+
+        # Notation (<variable name> -> <name in paper>
+        # - pred_noise_t -> e_theta(x_t, t)
+        # - pred_original_sample -> f_theta(x_t, t) or x_0
+        # - std_dev_t -> sigma_t
+        # - eta -> η
+        # - pred_sample_direction -> "direction pointing to x_t"
+        # - pred_prev_sample -> "x_t-1"
+
+        # 1. get previous step value (=t-1)
+        prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
+
+        # 2. compute alphas, betas
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+
+        beta_prod_t = 1 - alpha_prod_t
+
+        # 3. compute predicted original sample from predicted noise also called
+        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        if self.config.prediction_type == "epsilon":
+            pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
+            pred_epsilon = model_output
+        elif self.config.prediction_type == "sample":
+            pred_original_sample = model_output
+            pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+        elif self.config.prediction_type == "v_prediction":
+            pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
+            pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
+        else:
+            raise ValueError(
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
+                " `v_prediction`"
+            )
+
+        # 4. Clip or threshold "predicted x_0"
+        if self.config.clip_sample:
+            pred_original_sample = pred_original_sample.clamp(
+                -self.config.clip_sample_range, self.config.clip_sample_range
+            )
+
+        if self.config.thresholding:
+            pred_original_sample = self._threshold_sample(pred_original_sample)
+
+        # 5. compute variance: "sigma_t(η)" -> see formula (16)
+        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
+        variance = self._get_variance(timestep, prev_timestep)
+        std_dev_t = eta * variance ** (0.5)
+
+        if use_clipped_model_output:
+            # the pred_epsilon is always re-derived from the clipped x_0 in Glide
+            pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+
+        # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon
+
+        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
+
+        if eta > 0:
+            if variance_noise is not None and generator is not None:
+                raise ValueError(
+                    "Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
+                    " `variance_noise` stays `None`."
+                )
+
+            if variance_noise is None:
+                variance_noise = randn_tensor(
+                    model_output.shape, generator=generator, device=model_output.device, dtype=model_output.dtype
+                )
+            variance = std_dev_t * variance_noise
+
+            prev_sample = prev_sample + variance
+
+        if not return_dict:
+            return (prev_sample,)
+
+        return DDIMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)
+
+    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
+        self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device, dtype=original_samples.dtype)
+        timesteps = timesteps.to(original_samples.device)
+
+        sqrt_alpha_prod = self.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 - self.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
+
+    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
+        self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device, dtype=sample.dtype)
+        timesteps = timesteps.to(sample.device)
+
+        sqrt_alpha_prod = self.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 - self.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