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src/pfode_solver.py

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+import os, math, random, argparse, logging
+from pathlib import Path
+from typing import Optional, Union, List, Callable
+from collections import OrderedDict
+from packaging import version
+from tqdm.auto import tqdm
+from omegaconf import OmegaConf
+        
+import numpy as np
+import torch
+import torch.nn.functional as F
+import torch.utils.checkpoint
+import torchvision
+
+
+class PFODESolver():
+    def __init__(self, scheduler, t_initial=1, t_terminal=0,) -> None:
+        self.t_initial = t_initial
+        self.t_terminal = t_terminal
+        self.scheduler = scheduler
+
+        train_step_terminal = 0 
+        train_step_initial = train_step_terminal + self.scheduler.config.num_train_timesteps # 0+1000
+        
+        self.stepsize  = (t_terminal-t_initial) / (train_step_terminal - train_step_initial) #1/1000
+        
+    
+    def get_timesteps(self, t_start, t_end, num_steps):
+        # (b,) -> (b,1)
+        t_start = t_start[:, None]
+        t_end = t_end[:, None]
+        assert t_start.dim() == 2
+        
+        timepoints = torch.arange(0, num_steps, 1).expand(t_start.shape[0], num_steps).to(device=t_start.device)
+        interval = (t_end - t_start) / (torch.ones([1], device=t_start.device) * num_steps)
+        timepoints = t_start + interval * timepoints
+        
+        timesteps = (self.scheduler.num_train_timesteps - 1) + (timepoints - self.t_initial) / self.stepsize # correspondint to StableDiffusion indexing system, from 999 (t_init) -> 0 (dt)
+        return timesteps.round().long()
+        # return timesteps.floor().long()
+    
+    def solve(self, 
+              latents, 
+              unet, 
+              t_start, 
+              t_end, 
+              prompt_embeds, 
+              negative_prompt_embeds, 
+              guidance_scale=1.0,
+              num_steps = 2,
+              num_windows = 1,
+    ):
+        assert t_start.dim() == 1
+        assert guidance_scale >= 1 and torch.all(torch.gt(t_start, t_end))
+        
+        do_classifier_free_guidance = True if guidance_scale > 1 else False
+        bsz = latents.shape[0]
+            
+        if do_classifier_free_guidance:
+            prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds])
+            
+        timestep_cond = None
+        if unet.config.time_cond_proj_dim is not None:
+            guidance_scale_tensor = torch.tensor(guidance_scale - 1).repeat(bsz)
+            timestep_cond = self.get_guidance_scale_embedding(
+                guidance_scale_tensor, embedding_dim=unet.config.time_cond_proj_dim
+            ).to(device=latents.device, dtype=latents.dtype)
+            
+        
+        timesteps = self.get_timesteps(t_start, t_end, num_steps).to(device=latents.device)
+        timestep_interval = self.scheduler.config.num_train_timesteps // (num_windows * num_steps)
+
+        # 7. Denoising loop
+        with torch.no_grad():
+            # for i in tqdm(range(num_steps)):
+            for i in range(num_steps):
+                
+                t = torch.cat([timesteps[:, i]]*2) if do_classifier_free_guidance else timesteps[:, i]
+                # expand the latents if we are doing classifier free guidance
+                latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
+                latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
+
+                # predict the noise residual
+                noise_pred = unet(
+                    latent_model_input,
+                    t,
+                    encoder_hidden_states=prompt_embeds,
+                    timestep_cond=timestep_cond,
+                    return_dict=False,
+                )[0]
+
+                if do_classifier_free_guidance:
+                    noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
+                    noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
+
+
+                # STEP: compute the previous noisy sample x_t -> x_t-1
+                # latents = self.scheduler.step(noise_pred, timesteps[:, i].cpu(), latents, return_dict=False)[0]
+
+                batch_timesteps = timesteps[:, i].cpu()
+                prev_timestep = batch_timesteps - timestep_interval
+                # prev_timestep = batch_timesteps - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
+
+                alpha_prod_t = self.scheduler.alphas_cumprod[batch_timesteps]
+                alpha_prod_t_prev = torch.zeros_like(alpha_prod_t)
+                for ib in range(prev_timestep.shape[0]): 
+                    alpha_prod_t_prev[ib] = self.scheduler.alphas_cumprod[prev_timestep[ib]] if prev_timestep[ib] >= 0 else self.scheduler.final_alpha_cumprod
+                beta_prod_t = 1 - alpha_prod_t
+                
+                alpha_prod_t = alpha_prod_t.to(device=latents.device, dtype=latents.dtype)
+                alpha_prod_t_prev = alpha_prod_t_prev.to(device=latents.device, dtype=latents.dtype)
+                beta_prod_t = beta_prod_t.to(device=latents.device, dtype=latents.dtype)
+
+                # 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.scheduler.config.prediction_type == "epsilon":
+                    pred_original_sample = (latents - beta_prod_t[:,None,None,None] ** (0.5) * noise_pred) / alpha_prod_t[:, None,None,None] ** (0.5)
+                    pred_epsilon = noise_pred
+                # elif self.scheduler.config.prediction_type == "sample":
+                #     pred_original_sample = noise_pred
+                #     pred_epsilon = (latents - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+                elif self.scheduler.config.prediction_type == "v_prediction":
+                    pred_original_sample = (alpha_prod_t[:,None,None,None]**0.5) * latents - (beta_prod_t[:,None,None,None]**0.5) * noise_pred
+                    pred_epsilon = (alpha_prod_t[:,None,None,None]**0.5) * noise_pred + (beta_prod_t[:,None,None,None]**0.5) * latents
+                else:
+                    raise ValueError(
+                        f"prediction_type given as {self.scheduler.config.prediction_type} must be one of `epsilon`, `sample`, or"
+                        " `v_prediction`"
+                    )
+                    
+                pred_sample_direction = (1 - alpha_prod_t_prev[:,None,None,None]) ** (0.5) * pred_epsilon
+                latents = alpha_prod_t_prev[:,None,None,None] ** (0.5) * pred_original_sample + pred_sample_direction
+
+            
+        return latents
+    
+    
+    
+    
+    
+
+
+
+class PFODESolverSDXL():
+    def __init__(self, scheduler, t_initial=1, t_terminal=0,) -> None:
+        self.t_initial = t_initial
+        self.t_terminal = t_terminal
+        self.scheduler = scheduler
+
+        train_step_terminal = 0 
+        train_step_initial = train_step_terminal + self.scheduler.config.num_train_timesteps # 0+1000
+        
+        self.stepsize  = (t_terminal-t_initial) / (train_step_terminal - train_step_initial) #1/1000
+    
+    def get_timesteps(self, t_start, t_end, num_steps):
+        # (b,) -> (b,1)
+        t_start = t_start[:, None]
+        t_end = t_end[:, None]
+        assert t_start.dim() == 2
+        
+        timepoints = torch.arange(0, num_steps, 1).expand(t_start.shape[0], num_steps).to(device=t_start.device)
+        interval = (t_end - t_start) / (torch.ones([1], device=t_start.device) * num_steps)
+        timepoints = t_start + interval * timepoints
+        
+        timesteps = (self.scheduler.num_train_timesteps - 1) + (timepoints - self.t_initial) / self.stepsize # correspondint to StableDiffusion indexing system, from 999 (t_init) -> 0 (dt)
+        return timesteps.round().long()
+        # return timesteps.floor().long()
+    
+    def _get_add_time_ids(self, original_size, crops_coords_top_left, target_size, dtype):
+        # Adapted from pipeline.StableDiffusionXLPipeline._get_add_time_ids
+        add_time_ids = list(original_size + crops_coords_top_left + target_size)
+        add_time_ids = torch.tensor([add_time_ids], dtype=dtype)
+        return add_time_ids
+
+    def solve(self, 
+            latents, 
+            unet, 
+            t_start, 
+            t_end, 
+            prompt_embeds,
+            pooled_prompt_embeds,
+            negative_prompt_embeds,
+            negative_pooled_prompt_embeds,
+            guidance_scale=1.0,
+            num_steps = 10,
+            num_windows = 4,
+            resolution = 1024,
+    ):
+        assert t_start.dim() == 1
+        assert guidance_scale >= 1 and torch.all(torch.gt(t_start, t_end))
+        dtype = latents.dtype
+        device = latents.device
+        bsz = latents.shape[0]
+        do_classifier_free_guidance = True if guidance_scale > 1 else False
+        
+        add_text_embeds = pooled_prompt_embeds
+        add_time_ids = torch.cat(
+            # [self._get_add_time_ids((1024, 1024), (0, 0), (1024, 1024), dtype) for _ in range(bsz)]
+            [self._get_add_time_ids((resolution, resolution), (0, 0), (resolution, resolution), dtype) for _ in range(bsz)]
+        ).to(device)
+        negative_add_time_ids = add_time_ids
+        
+        if do_classifier_free_guidance:
+            # prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds])
+            prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds], dim=0)
+            add_text_embeds = torch.cat([negative_pooled_prompt_embeds, add_text_embeds], dim=0)
+            add_time_ids = torch.cat([negative_add_time_ids, add_time_ids], dim=0)
+            
+        timestep_cond = None
+        if unet.config.time_cond_proj_dim is not None:
+            guidance_scale_tensor = torch.tensor(guidance_scale - 1).repeat(bsz)
+            timestep_cond = self.get_guidance_scale_embedding(
+                guidance_scale_tensor, embedding_dim=unet.config.time_cond_proj_dim
+            ).to(device=latents.device, dtype=latents.dtype)
+            
+        
+        timesteps = self.get_timesteps(t_start, t_end, num_steps).to(device=latents.device)
+        timestep_interval = self.scheduler.config.num_train_timesteps // (num_windows * num_steps)
+
+        # 7. Denoising loop
+        with torch.no_grad():
+            # for i in tqdm(range(num_steps)):
+            for i in range(num_steps):
+                # expand the latents if we are doing classifier free guidance
+                t = torch.cat([timesteps[:, i]]*2) if do_classifier_free_guidance else timesteps[:, i]
+                latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
+                latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
+
+                # predict the noise residual
+                added_cond_kwargs = {"text_embeds": add_text_embeds, "time_ids": add_time_ids}
+                noise_pred = unet(
+                    latent_model_input,
+                    t,
+                    encoder_hidden_states=prompt_embeds,
+                    timestep_cond=timestep_cond,
+                    added_cond_kwargs=added_cond_kwargs,
+                    return_dict=False,
+                )[0]
+
+                if do_classifier_free_guidance:
+                    noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
+                    noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
+
+
+                # STEP: compute the previous noisy sample x_t -> x_t-1
+                # latents = self.scheduler.step(noise_pred, timesteps[:, i].cpu(), latents, return_dict=False)[0]
+
+                batch_timesteps = timesteps[:, i].cpu()
+                prev_timestep = batch_timesteps - timestep_interval
+                # prev_timestep = batch_timesteps - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
+
+                alpha_prod_t = self.scheduler.alphas_cumprod[batch_timesteps]
+                alpha_prod_t_prev = torch.zeros_like(alpha_prod_t)
+                for ib in range(prev_timestep.shape[0]): 
+                    alpha_prod_t_prev[ib] = self.scheduler.alphas_cumprod[prev_timestep[ib]] if prev_timestep[ib] >= 0 else self.scheduler.final_alpha_cumprod
+                beta_prod_t = 1 - alpha_prod_t
+                
+                alpha_prod_t = alpha_prod_t.to(device=latents.device, dtype=latents.dtype)
+                alpha_prod_t_prev = alpha_prod_t_prev.to(device=latents.device, dtype=latents.dtype)
+                beta_prod_t = beta_prod_t.to(device=latents.device, dtype=latents.dtype)
+
+                # 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.scheduler.config.prediction_type == "epsilon":
+                    pred_original_sample = (latents - beta_prod_t[:,None,None,None] ** (0.5) * noise_pred) / alpha_prod_t[:, None,None,None] ** (0.5)
+                    pred_epsilon = noise_pred
+                # elif self.scheduler.config.prediction_type == "sample":
+                #     pred_original_sample = noise_pred
+                #     pred_epsilon = (latents - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+                # elif self.scheduler.config.prediction_type == "v_prediction":
+                #     pred_original_sample = (alpha_prod_t**0.5) * latents - (beta_prod_t**0.5) * noise_pred
+                #     pred_epsilon = (alpha_prod_t**0.5) * noise_pred + (beta_prod_t**0.5) * latents
+                else:
+                    raise ValueError(
+                        f"prediction_type given as {self.scheduler.config.prediction_type} must be one of `epsilon`, `sample`, or"
+                        " `v_prediction`"
+                    )
+                    
+                pred_sample_direction = (1 - alpha_prod_t_prev[:,None,None,None]) ** (0.5) * pred_epsilon
+                latents = alpha_prod_t_prev[:,None,None,None] ** (0.5) * pred_original_sample + pred_sample_direction
+
+            
+        return latents

src/scheduler_perflow.py

@@ -0,0 +1,377 @@
+# 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 diffusers.configuration_utils import ConfigMixin, register_to_config
+from diffusers.utils import BaseOutput
+from diffusers.utils.torch_utils import randn_tensor
+from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
+
+
+class Time_Windows():
+    def __init__(self, t_initial=1, t_terminal=0, num_windows=4, precision=1./1000) -> None:
+        assert t_terminal < t_initial
+        time_windows = [ 1.*i/num_windows for i in range(1, num_windows+1)][::-1]
+        
+        self.window_starts = time_windows                      # [1.0, 0.75, 0.5, 0.25]
+        self.window_ends = time_windows[1:] + [t_terminal]     # [0.75, 0.5, 0.25, 0]
+        self.precision = precision
+    
+    def get_window(self, tp):
+        idx = 0
+        # robust to numerical error; e.g, (0.6+1/10000) belongs to [0.6, 0.3)
+        while (tp-0.1*self.precision) <= self.window_ends[idx]: 
+            idx += 1
+        return self.window_starts[idx], self.window_ends[idx]
+    
+    def lookup_window(self, timepoint):
+        if timepoint.dim() == 0:
+            t_start, t_end = self.get_window(timepoint)
+            t_start = torch.ones_like(timepoint) * t_start
+            t_end = torch.ones_like(timepoint) * t_end
+        else:
+            t_start = torch.zeros_like(timepoint)
+            t_end = torch.zeros_like(timepoint)
+            bsz = timepoint.shape[0]
+            for i in range(bsz):
+                tp = timepoint[i]
+                ts, te = self.get_window(tp)
+                t_start[i] = ts
+                t_end[i] = te
+        return t_start, t_end
+    
+
+@dataclass
+class PeRFlowSchedulerOutput(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)
+
+
+
+class PeRFlowScheduler(SchedulerMixin, ConfigMixin):
+    """
+    `ReFlowScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with
+    non-Markovian guidance.
+
+    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`.
+        trained_betas (`np.ndarray`, *optional*):
+            Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
+        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*)
+    """
+
+    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
+    order = 1
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.00085,
+        beta_end: float = 0.012,
+        beta_schedule: str = "scaled_linear",
+        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
+        set_alpha_to_one: bool = False,
+        prediction_type: str = "ddim_eps",
+        t_noise: float = 1,
+        t_clean: float = 0,
+        num_time_windows = 4,
+    ):
+        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
+
+        self.time_windows = Time_Windows(t_initial=t_noise, t_terminal=t_clean, 
+                                         num_windows=num_time_windows, 
+                                         precision=1./num_train_timesteps)
+        
+        assert prediction_type in ["ddim_eps", "diff_eps", "velocity"]
+
+
+    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: int, device: Union[str, torch.device] = 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 num_inference_steps < self.config.num_time_windows:
+            num_inference_steps = self.config.num_time_windows
+            print(f"### We recommend a num_inference_steps not less than num_time_windows. It's set as {self.config.num_time_windows}.")
+
+        timesteps = []
+        for i in range(self.config.num_time_windows):
+            if i < num_inference_steps%self.config.num_time_windows:
+                num_steps_cur_win = num_inference_steps//self.config.num_time_windows+1
+            else:
+                num_steps_cur_win = num_inference_steps//self.config.num_time_windows
+
+            t_s = self.time_windows.window_starts[i]
+            t_e = self.time_windows.window_ends[i]
+            timesteps_cur_win = np.linspace(t_s, t_e, num=num_steps_cur_win, endpoint=False)
+            timesteps.append(timesteps_cur_win)
+                        
+        timesteps = np.concatenate(timesteps)
+
+        self.timesteps = torch.from_numpy(
+            (timesteps*self.config.num_train_timesteps).astype(np.int64)
+        ).to(device)
+            
+    def get_window_alpha(self, timepoints):
+        time_windows = self.time_windows
+        num_train_timesteps = self.config.num_train_timesteps
+        
+        t_win_start, t_win_end = time_windows.lookup_window(timepoints)
+        t_win_len = t_win_end - t_win_start
+        t_interval = timepoints - t_win_start # NOTE: negative value
+
+        idx_start = (t_win_start*num_train_timesteps - 1 ).long()
+        alphas_cumprod_start = self.alphas_cumprod[idx_start]
+        
+        idx_end = torch.clamp( (t_win_end*num_train_timesteps - 1 ).long(), min=0)  #FIXME:
+        alphas_cumprod_end = self.alphas_cumprod[idx_end]
+
+        alpha_cumprod_s_e = alphas_cumprod_start / alphas_cumprod_end      
+        gamma_s_e = alpha_cumprod_s_e ** 0.5
+        
+        return t_win_start, t_win_end, t_win_len, t_interval, gamma_s_e, alphas_cumprod_start, alphas_cumprod_end 
+        
+    def step(
+        self,
+        model_output: torch.FloatTensor,
+        timestep: int,
+        sample: torch.FloatTensor,
+        return_dict: bool = True,
+    ) -> Union[PeRFlowSchedulerOutput, 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.
+            return_dict (`bool`, *optional*, defaults to `True`):
+                Whether or not to return a [`~schedulers.scheduling_ddim.PeRFlowSchedulerOutput`] or `tuple`.
+
+        Returns:
+            [`~schedulers.scheduling_utils.PeRFlowSchedulerOutput`] or `tuple`:
+                If return_dict is `True`, [`~schedulers.scheduling_ddim.PeRFlowSchedulerOutput`] is returned, otherwise a
+                tuple is returned where the first element is the sample tensor.
+        """
+
+        if self.config.prediction_type == "ddim_eps":
+            pred_epsilon = model_output
+            t_c = timestep / self.config.num_train_timesteps
+            t_s, t_e, _, c_to_s, _, alphas_cumprod_start, alphas_cumprod_end = self.get_window_alpha(t_c)
+            
+            lambda_s = (alphas_cumprod_end / alphas_cumprod_start)**0.5
+            eta_s = (1-alphas_cumprod_end)**0.5 - ( alphas_cumprod_end / alphas_cumprod_start * (1-alphas_cumprod_start) )**0.5
+            
+            lambda_t =  ( lambda_s * (t_e - t_s) ) / ( lambda_s *(t_c - t_s) + (t_e - t_c) )
+            eta_t = ( eta_s * (t_e - t_c) ) / ( lambda_s *(t_c - t_s) + (t_e - t_c) )
+            
+            pred_win_end = lambda_t * sample + eta_t * pred_epsilon
+            pred_velocity = (pred_win_end - sample) / (t_e - (t_s + c_to_s))
+            
+        # elif self.config.prediction_type == "diff_eps":
+        #     pred_epsilon = model_output
+        #     t_c = timestep / self.config.num_train_timesteps
+        #     t_s, t_e, win_len, c_to_s, gamma_s_e, _, _ = self.get_window_alpha(t_c)
+        #     pred_sample_end = ( sample - (1-c_to_s/win_len) * ((1-gamma_s_e**2)**0.5) * pred_epsilon ) \
+        #         / ( gamma_s_e + c_to_s / win_len * (1-gamma_s_e) )
+        #     pred_velocity = (pred_sample_end - sample) / (t_e - (t_s + c_to_s))
+            
+        elif self.config.prediction_type == "diff_eps":
+            pred_epsilon = model_output
+            t_c = timestep / self.config.num_train_timesteps
+            t_s, t_e, _, c_to_s, gamma_s_e, _, _ = self.get_window_alpha(t_c)
+            
+            lambda_s = 1 / gamma_s_e
+            eta_s = -1 * ( 1- gamma_s_e**2)**0.5 / gamma_s_e
+            
+            lambda_t =  ( lambda_s * (t_e - t_s) ) / ( lambda_s *(t_c - t_s) + (t_e - t_c) )
+            eta_t = ( eta_s * (t_e - t_c) ) / ( lambda_s *(t_c - t_s) + (t_e - t_c) )
+            
+            pred_win_end = lambda_t * sample + eta_t * pred_epsilon
+            pred_velocity = (pred_win_end - sample) / (t_e - (t_s + c_to_s))
+
+        elif self.config.prediction_type == "velocity":
+            pred_velocity = model_output
+        else:
+            raise ValueError(
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `velocity`."
+            )
+            
+        # get dt
+        idx = torch.argwhere(torch.where(self.timesteps==timestep, 1,0))
+        prev_step = self.timesteps[idx+1] if (idx+1)<len(self.timesteps) else 0
+        dt = (prev_step - timestep) / self.config.num_train_timesteps
+        dt = dt.to(sample.device, sample.dtype)
+
+        prev_sample = sample + dt * pred_velocity
+
+        if not return_dict:
+            return (prev_sample,)
+        return PeRFlowSchedulerOutput(prev_sample=prev_sample, pred_original_sample=None)
+
+
+    # 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) - 1   # indexing from 0
+
+        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
+
+    def __len__(self):
+        return self.config.num_train_timesteps

src/utils_perflow.py

@@ -0,0 +1,77 @@
+import os
+from collections import OrderedDict
+import torch
+from safetensors import safe_open
+from safetensors.torch import save_file
+from diffusers.pipelines.stable_diffusion import StableDiffusionPipeline
+from diffusers.pipelines.stable_diffusion.convert_from_ckpt import convert_ldm_unet_checkpoint, convert_ldm_vae_checkpoint, convert_ldm_clip_checkpoint
+    
+
+def merge_delta_weights_into_unet(pipe, delta_weights):
+    unet_weights = pipe.unet.state_dict()
+    assert unet_weights.keys() == delta_weights.keys()
+    for key in delta_weights.keys():
+        dtype = unet_weights[key].dtype
+        unet_weights[key] = unet_weights[key].to(dtype=delta_weights[key].dtype) + delta_weights[key].to(device=unet_weights[key].device)
+        unet_weights[key] = unet_weights[key].to(dtype)
+    pipe.unet.load_state_dict(unet_weights, strict=True)
+    return pipe
+
+
+def load_delta_weights_into_unet(
+    pipe, 
+    model_path = "hsyan/piecewise-rectified-flow-v0-1", 
+    base_path = "runwayml/stable-diffusion-v1-5",
+):
+    ## load delta_weights
+    if os.path.exists(os.path.join(model_path, "delta_weights.safetensors")):
+        print("### delta_weights exists, loading...")
+        delta_weights = OrderedDict()
+        with safe_open(os.path.join(model_path, "delta_weights.safetensors"), framework="pt", device="cpu") as f:
+            for key in f.keys():
+                delta_weights[key] = f.get_tensor(key)
+                
+    elif os.path.exists(os.path.join(model_path, "diffusion_pytorch_model.safetensors")):
+        print("### merged_weights exists, loading...")
+        merged_weights = OrderedDict()
+        with safe_open(os.path.join(model_path, "diffusion_pytorch_model.safetensors"), framework="pt", device="cpu") as f:
+            for key in f.keys():
+                merged_weights[key] = f.get_tensor(key)
+                
+        base_weights = StableDiffusionPipeline.from_pretrained(
+            base_path, torch_dtype=torch.float16, safety_checker=None).unet.state_dict()
+        assert base_weights.keys() == merged_weights.keys()
+        
+        delta_weights = OrderedDict()
+        for key in merged_weights.keys():
+            delta_weights[key] = merged_weights[key] - base_weights[key].to(device=merged_weights[key].device, dtype=merged_weights[key].dtype)
+        
+        print("### saving delta_weights...")
+        save_file(delta_weights, os.path.join(model_path, "delta_weights.safetensors"))
+        
+    else:
+        raise ValueError(f"{model_path} does not contain delta weights or merged weights")
+        
+    ## merge delta_weights to the target pipeline
+    pipe = merge_delta_weights_into_unet(pipe, delta_weights)
+    return pipe
+    
+
+
+
+def load_dreambooth_into_pipeline(pipe, sd_dreambooth):
+    assert sd_dreambooth.endswith(".safetensors")
+    state_dict = {}
+    with safe_open(sd_dreambooth, framework="pt", device="cpu") as f:
+        for key in f.keys():
+            state_dict[key] = f.get_tensor(key)
+    
+    unet_config = {} # unet, line 449 in convert_ldm_unet_checkpoint
+    for key in pipe.unet.config.keys():
+        if key != 'num_class_embeds':
+            unet_config[key] = pipe.unet.config[key]
+            
+    pipe.unet.load_state_dict(convert_ldm_unet_checkpoint(state_dict, unet_config), strict=False)
+    pipe.vae.load_state_dict(convert_ldm_vae_checkpoint(state_dict, pipe.vae.config))
+    pipe.text_encoder = convert_ldm_clip_checkpoint(state_dict, text_encoder=pipe.text_encoder)
+    return pipe