Create scheduling_ddim.py

scheduling_ddim.py

@@ -0,0 +1,404 @@
+# adapted and updated from https://github.com/huggingface/diffusers/blob/main/src/diffusers/schedulers/scheduling_ddim.py
+
+# Copyright 2022 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 Optional, Tuple, Union
+
+import numpy as np
+import torch
+import matplotlib.pyplot as plt
+from tqdm.auto import tqdm
+from PIL import Image
+
+from diffusers.configuration_utils import ConfigMixin, register_to_config
+from diffusers.utils import BaseOutput, deprecate
+from diffusers.schedulers.scheduling_utils import SchedulerMixin
+
+
+@dataclass
+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.
+        next_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
+            Computed sample (x_{t+1}) of previous timestep. `next_sample` should be used as next model input in the
+            reverse 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: Optional[torch.FloatTensor] = None
+    next_sample: Optional[torch.FloatTensor] = None
+    pred_original_sample: Optional[torch.FloatTensor] = None
+
+
+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)
+
+
+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`.
+    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
+    [`~ConfigMixin.from_config`] 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 between -1 and 1 for numerical stability.
+        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.
+
+    """
+
+    @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[np.ndarray] = None,
+        clip_sample: bool = True,
+        set_alpha_to_one: bool = True,
+        steps_offset: int = 0,
+    ):
+        if trained_betas is not None:
+            self.betas = torch.from_numpy(trained_betas)
+        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 _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
+
+    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.
+        """
+        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 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 step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        eta: float = 0.0,
+        use_clipped_model_output: bool = False,
+        generator=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`): TODO
+            generator: random number generator.
+            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 ( -> 
+        # - 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
+        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
+
+        # 4. Clip "predicted x_0"
+        if self.config.clip_sample:
+            pred_original_sample = torch.clamp(pred_original_sample, -1, 1)
+
+        # 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 model_output is always re-derived from the clipped x_0 in Glide
+            model_output = (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) * model_output
+
+        # 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:
+            device = model_output.device if torch.is_tensor(model_output) else "cpu"
+            noise = torch.randn(model_output.shape, generator=generator).to(device)
+            variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * 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 reverse_step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        eta: float = 0.0,
+        use_clipped_model_output: bool = False,
+        generator=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`): TODO
+            generator: random number generator.
+            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 ( -> 
+        # - 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)
+        next_timestep = min(self.config.num_train_timesteps - 2,
+                            timestep + self.config.num_train_timesteps // self.num_inference_steps)
+
+        # 2. compute alphas, betas
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_next = self.alphas_cumprod[next_timestep] if next_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
+        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
+
+        # 4. Clip "predicted x_0"
+        if self.config.clip_sample:
+            pred_original_sample = torch.clamp(pred_original_sample, -1, 1)
+
+        # 5. TODO: simple noising implementatiom
+        next_sample = self.add_noise(pred_original_sample,
+                                     model_output,
+                                     torch.LongTensor([next_timestep]))
+
+        # # 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(next_timestep, timestep)
+        # std_dev_t = eta * variance ** (0.5)
+
+        # if use_clipped_model_output:
+        #     # the model_output is always re-derived from the clipped x_0 in Glide
+        #     model_output = (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_next - std_dev_t**2) ** (0.5) * model_output
+
+        # # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        # next_sample = alpha_prod_t_next ** (0.5) * pred_original_sample + pred_sample_direction
+
+        if not return_dict:
+            return (next_sample,)
+
+        return DDIMSchedulerOutput(next_sample=next_sample, pred_original_sample=pred_original_sample)
+
+    def add_noise(
+        self,
+        original_samples: torch.FloatTensor,
+        noise: torch.FloatTensor,
+        timesteps: torch.IntTensor,
+    ) -> torch.FloatTensor:
+        if self.alphas_cumprod.device != original_samples.device:
+            self.alphas_cumprod = self.alphas_cumprod.to(original_samples.device)
+        if timesteps.device != original_samples.device:
+            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 __len__(self):
+        return self.config.num_train_timesteps