# Copyright 2023 TSAIL 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/LuChengTHU/dpm-solver from dataclasses import dataclass from typing import List, Optional, Tuple, Union import flax import jax import jax.numpy as jnp from ..configuration_utils import ConfigMixin, register_to_config from .scheduling_utils_flax import ( CommonSchedulerState, FlaxKarrasDiffusionSchedulers, FlaxSchedulerMixin, FlaxSchedulerOutput, add_noise_common, ) @flax.struct.dataclass class DPMSolverMultistepSchedulerState: common: CommonSchedulerState alpha_t: jnp.ndarray sigma_t: jnp.ndarray lambda_t: jnp.ndarray # setable values init_noise_sigma: jnp.ndarray timesteps: jnp.ndarray num_inference_steps: Optional[int] = None # running values model_outputs: Optional[jnp.ndarray] = None lower_order_nums: Optional[jnp.int32] = None prev_timestep: Optional[jnp.int32] = None cur_sample: Optional[jnp.ndarray] = None @classmethod def create( cls, common: CommonSchedulerState, alpha_t: jnp.ndarray, sigma_t: jnp.ndarray, lambda_t: jnp.ndarray, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, ): return cls( common=common, alpha_t=alpha_t, sigma_t=sigma_t, lambda_t=lambda_t, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) @dataclass class FlaxDPMSolverMultistepSchedulerOutput(FlaxSchedulerOutput): state: DPMSolverMultistepSchedulerState class FlaxDPMSolverMultistepScheduler(FlaxSchedulerMixin, ConfigMixin): """ DPM-Solver (and the improved version DPM-Solver++) is a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. Empirically, sampling by DPM-Solver with only 20 steps can generate high-quality samples, and it can generate quite good samples even in only 10 steps. For more details, see the original paper: https://arxiv.org/abs/2206.00927 and https://arxiv.org/abs/2211.01095 Currently, we support the multistep DPM-Solver for both noise prediction models and data prediction models. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling. We also support the "dynamic thresholding" method in Imagen (https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type="dpmsolver++"` and `thresholding=True` to use the dynamic thresholding. Note that the thresholding method is unsuitable for latent-space diffusion models (such as stable-diffusion). [`~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/2206.00927 and https://arxiv.org/abs/2211.01095 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. solver_order (`int`, default `2`): the order of DPM-Solver; can be `1` or `2` or `3`. We recommend to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling. prediction_type (`str`, default `epsilon`): indicates whether the model predicts the noise (epsilon), or the data / `x0`. One of `epsilon`, `sample`, or `v-prediction`. thresholding (`bool`, default `False`): whether to use the "dynamic thresholding" method (introduced by Imagen, https://arxiv.org/abs/2205.11487). For pixel-space diffusion models, you can set both `algorithm_type=dpmsolver++` and `thresholding=True` to use the dynamic thresholding. 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). sample_max_value (`float`, default `1.0`): the threshold value for dynamic thresholding. Valid only when `thresholding=True` and `algorithm_type="dpmsolver++`. algorithm_type (`str`, default `dpmsolver++`): the algorithm type for the solver. Either `dpmsolver` or `dpmsolver++`. The `dpmsolver` type implements the algorithms in https://arxiv.org/abs/2206.00927, and the `dpmsolver++` type implements the algorithms in https://arxiv.org/abs/2211.01095. We recommend to use `dpmsolver++` with `solver_order=2` for guided sampling (e.g. stable-diffusion). solver_type (`str`, default `midpoint`): the solver type for the second-order solver. Either `midpoint` or `heun`. The solver type slightly affects the sample quality, especially for small number of steps. We empirically find that `midpoint` solvers are slightly better, so we recommend to use the `midpoint` type. lower_order_final (`bool`, default `True`): whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. We empirically find this trick can stabilize the sampling of DPM-Solver for steps < 15, especially for steps <= 10. timestep_spacing (`str`, defaults to `"linspace"`): 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. dtype (`jnp.dtype`, *optional*, defaults to `jnp.float32`): the `dtype` used for params and computation. """ _compatibles = [e.name for e in FlaxKarrasDiffusionSchedulers] dtype: jnp.dtype @property def has_state(self): return True @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[jnp.ndarray] = None, solver_order: int = 2, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, algorithm_type: str = "dpmsolver++", solver_type: str = "midpoint", lower_order_final: bool = True, timestep_spacing: str = "linspace", dtype: jnp.dtype = jnp.float32, ): self.dtype = dtype def create_state(self, common: Optional[CommonSchedulerState] = None) -> DPMSolverMultistepSchedulerState: if common is None: common = CommonSchedulerState.create(self) # Currently we only support VP-type noise schedule alpha_t = jnp.sqrt(common.alphas_cumprod) sigma_t = jnp.sqrt(1 - common.alphas_cumprod) lambda_t = jnp.log(alpha_t) - jnp.log(sigma_t) # settings for DPM-Solver if self.config.algorithm_type not in ["dpmsolver", "dpmsolver++"]: raise NotImplementedError(f"{self.config.algorithm_type} does is not implemented for {self.__class__}") if self.config.solver_type not in ["midpoint", "heun"]: raise NotImplementedError(f"{self.config.solver_type} does is not implemented for {self.__class__}") # standard deviation of the initial noise distribution init_noise_sigma = jnp.array(1.0, dtype=self.dtype) timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1] return DPMSolverMultistepSchedulerState.create( common=common, alpha_t=alpha_t, sigma_t=sigma_t, lambda_t=lambda_t, init_noise_sigma=init_noise_sigma, timesteps=timesteps, ) def set_timesteps( self, state: DPMSolverMultistepSchedulerState, num_inference_steps: int, shape: Tuple ) -> DPMSolverMultistepSchedulerState: """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference. Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. num_inference_steps (`int`): the number of diffusion steps used when generating samples with a pre-trained model. shape (`Tuple`): the shape of the samples to be generated. """ last_timestep = self.config.num_train_timesteps if self.config.timestep_spacing == "linspace": timesteps = ( jnp.linspace(0, last_timestep - 1, num_inference_steps + 1).round()[::-1][:-1].astype(jnp.int32) ) elif self.config.timestep_spacing == "leading": step_ratio = last_timestep // (num_inference_steps + 1) # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = ( (jnp.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(jnp.int32) ) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / 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 = jnp.arange(last_timestep, 0, -step_ratio).round().copy().astype(jnp.int32) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'." ) # initial running values model_outputs = jnp.zeros((self.config.solver_order,) + shape, dtype=self.dtype) lower_order_nums = jnp.int32(0) prev_timestep = jnp.int32(-1) cur_sample = jnp.zeros(shape, dtype=self.dtype) return state.replace( num_inference_steps=num_inference_steps, timesteps=timesteps, model_outputs=model_outputs, lower_order_nums=lower_order_nums, prev_timestep=prev_timestep, cur_sample=cur_sample, ) def convert_model_output( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ Convert the model output to the corresponding type that the algorithm (DPM-Solver / DPM-Solver++) needs. DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an integral of the data prediction model. So we need to first convert the model output to the corresponding type to match the algorithm. Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or DPM-Solver++ for both noise prediction model and data prediction model. Args: model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. Returns: `jnp.ndarray`: the converted model output. """ # DPM-Solver++ needs to solve an integral of the data prediction model. if self.config.algorithm_type == "dpmsolver++": if self.config.prediction_type == "epsilon": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] x0_pred = (sample - sigma_t * model_output) / alpha_t elif self.config.prediction_type == "sample": x0_pred = model_output elif self.config.prediction_type == "v_prediction": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] x0_pred = alpha_t * sample - sigma_t * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, " " or `v_prediction` for the FlaxDPMSolverMultistepScheduler." ) if self.config.thresholding: # Dynamic thresholding in https://arxiv.org/abs/2205.11487 dynamic_max_val = jnp.percentile( jnp.abs(x0_pred), self.config.dynamic_thresholding_ratio, axis=tuple(range(1, x0_pred.ndim)) ) dynamic_max_val = jnp.maximum( dynamic_max_val, self.config.sample_max_value * jnp.ones_like(dynamic_max_val) ) x0_pred = jnp.clip(x0_pred, -dynamic_max_val, dynamic_max_val) / dynamic_max_val return x0_pred # DPM-Solver needs to solve an integral of the noise prediction model. elif self.config.algorithm_type == "dpmsolver": if self.config.prediction_type == "epsilon": return model_output elif self.config.prediction_type == "sample": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] epsilon = (sample - alpha_t * model_output) / sigma_t return epsilon elif self.config.prediction_type == "v_prediction": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] epsilon = alpha_t * model_output + sigma_t * sample return epsilon else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, " " or `v_prediction` for the FlaxDPMSolverMultistepScheduler." ) def dpm_solver_first_order_update( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the first-order DPM-Solver (equivalent to DDIM). See https://arxiv.org/abs/2206.00927 for the detailed derivation. Args: model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0 = prev_timestep, timestep m0 = model_output lambda_t, lambda_s = state.lambda_t[t], state.lambda_t[s0] alpha_t, alpha_s = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s = state.sigma_t[t], state.sigma_t[s0] h = lambda_t - lambda_s if self.config.algorithm_type == "dpmsolver++": x_t = (sigma_t / sigma_s) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * m0 elif self.config.algorithm_type == "dpmsolver": x_t = (alpha_t / alpha_s) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * m0 return x_t def multistep_dpm_solver_second_order_update( self, state: DPMSolverMultistepSchedulerState, model_output_list: jnp.ndarray, timestep_list: List[int], prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the second-order multistep DPM-Solver. Args: model_output_list (`List[jnp.ndarray]`): direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2] m0, m1 = model_output_list[-1], model_output_list[-2] lambda_t, lambda_s0, lambda_s1 = state.lambda_t[t], state.lambda_t[s0], state.lambda_t[s1] alpha_t, alpha_s0 = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s0 = state.sigma_t[t], state.sigma_t[s0] h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1 r0 = h_0 / h D0, D1 = m0, (1.0 / r0) * (m0 - m1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2211.01095 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 - 0.5 * (alpha_t * (jnp.exp(-h) - 1.0)) * D1 ) elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 + (alpha_t * ((jnp.exp(-h) - 1.0) / h + 1.0)) * D1 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - 0.5 * (sigma_t * (jnp.exp(h) - 1.0)) * D1 ) elif self.config.solver_type == "heun": x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - (sigma_t * ((jnp.exp(h) - 1.0) / h - 1.0)) * D1 ) return x_t def multistep_dpm_solver_third_order_update( self, state: DPMSolverMultistepSchedulerState, model_output_list: jnp.ndarray, timestep_list: List[int], prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the third-order multistep DPM-Solver. Args: model_output_list (`List[jnp.ndarray]`): direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3] m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3] lambda_t, lambda_s0, lambda_s1, lambda_s2 = ( state.lambda_t[t], state.lambda_t[s0], state.lambda_t[s1], state.lambda_t[s2], ) alpha_t, alpha_s0 = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s0 = state.sigma_t[t], state.sigma_t[s0] h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2 r0, r1 = h_0 / h, h_1 / h D0 = m0 D1_0, D1_1 = (1.0 / r0) * (m0 - m1), (1.0 / r1) * (m1 - m2) D1 = D1_0 + (r0 / (r0 + r1)) * (D1_0 - D1_1) D2 = (1.0 / (r0 + r1)) * (D1_0 - D1_1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2206.00927 for detailed derivations x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 + (alpha_t * ((jnp.exp(-h) - 1.0) / h + 1.0)) * D1 - (alpha_t * ((jnp.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - (sigma_t * ((jnp.exp(h) - 1.0) / h - 1.0)) * D1 - (sigma_t * ((jnp.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2 ) return x_t def step( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, return_dict: bool = True, ) -> Union[FlaxDPMSolverMultistepSchedulerOutput, Tuple]: """ Predict the sample at the previous timestep by DPM-Solver. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise). Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. return_dict (`bool`): option for returning tuple rather than FlaxDPMSolverMultistepSchedulerOutput class Returns: [`FlaxDPMSolverMultistepSchedulerOutput`] or `tuple`: [`FlaxDPMSolverMultistepSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ if state.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) (step_index,) = jnp.where(state.timesteps == timestep, size=1) step_index = step_index[0] prev_timestep = jax.lax.select(step_index == len(state.timesteps) - 1, 0, state.timesteps[step_index + 1]) model_output = self.convert_model_output(state, model_output, timestep, sample) model_outputs_new = jnp.roll(state.model_outputs, -1, axis=0) model_outputs_new = model_outputs_new.at[-1].set(model_output) state = state.replace( model_outputs=model_outputs_new, prev_timestep=prev_timestep, cur_sample=sample, ) def step_1(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: return self.dpm_solver_first_order_update( state, state.model_outputs[-1], state.timesteps[step_index], state.prev_timestep, state.cur_sample, ) def step_23(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: def step_2(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: timestep_list = jnp.array([state.timesteps[step_index - 1], state.timesteps[step_index]]) return self.multistep_dpm_solver_second_order_update( state, state.model_outputs, timestep_list, state.prev_timestep, state.cur_sample, ) def step_3(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: timestep_list = jnp.array( [ state.timesteps[step_index - 2], state.timesteps[step_index - 1], state.timesteps[step_index], ] ) return self.multistep_dpm_solver_third_order_update( state, state.model_outputs, timestep_list, state.prev_timestep, state.cur_sample, ) step_2_output = step_2(state) step_3_output = step_3(state) if self.config.solver_order == 2: return step_2_output elif self.config.lower_order_final and len(state.timesteps) < 15: return jax.lax.select( state.lower_order_nums < 2, step_2_output, jax.lax.select( step_index == len(state.timesteps) - 2, step_2_output, step_3_output, ), ) else: return jax.lax.select( state.lower_order_nums < 2, step_2_output, step_3_output, ) step_1_output = step_1(state) step_23_output = step_23(state) if self.config.solver_order == 1: prev_sample = step_1_output elif self.config.lower_order_final and len(state.timesteps) < 15: prev_sample = jax.lax.select( state.lower_order_nums < 1, step_1_output, jax.lax.select( step_index == len(state.timesteps) - 1, step_1_output, step_23_output, ), ) else: prev_sample = jax.lax.select( state.lower_order_nums < 1, step_1_output, step_23_output, ) state = state.replace( lower_order_nums=jnp.minimum(state.lower_order_nums + 1, self.config.solver_order), ) if not return_dict: return (prev_sample, state) return FlaxDPMSolverMultistepSchedulerOutput(prev_sample=prev_sample, state=state) def scale_model_input( self, state: DPMSolverMultistepSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None ) -> jnp.ndarray: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. sample (`jnp.ndarray`): input sample timestep (`int`, optional): current timestep Returns: `jnp.ndarray`: scaled input sample """ return sample def add_noise( self, state: DPMSolverMultistepSchedulerState, original_samples: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return add_noise_common(state.common, original_samples, noise, timesteps) def __len__(self): return self.config.num_train_timesteps