2、 Scheduler介绍代码解析 [代码级手把手解diffusers库]

- Scheduler简介
- 分类
- - 老式 ODE 求解器（Old-School ODE solvers）
  - 初始采样器（Ancestral samplers）
  - Karras噪声调度计划
  - DDIM和PLMS
  - DPM、DPM adaptive、DPM2和 DPM++
  - UniPC
  - k-diffusion
- 1.DDPM
- 2.DDIM
- 3.Euler
- 4.DPM系列
- 5. Ancestral
- 6. Karras
- 7. SDE

Scheduler简介

Diffusion Pipeline 本质上是彼此部分独立的模型和调度器的集合。Diffusion中最重要的我觉得一定是Scheduler，因为它这里面包含了扩散模型的基本原理，通过对代码的分析我们可以对论文中的公式有着更好的理解，同时diffusers也在DDPM的基础上优化了许多不同的scheduler版本，加深对这些scheduler的理解也可以帮助我们在实际选择scheduler时有更好的理论支持：

在这里插入图片描述
Scheduler直观上理解的话它就是一个采样器，循环多个step把噪声图像逐渐还原为原始图像(xt -> x0)。根据采样方式不同，scheduler也有许多版本，包括DDPM，DDIM，DPM++ 2M Karras等，通常决定了去噪速度和去噪质量。注意：看下面内容前最好对扩散模型的原理有一定了解，可参考论文DDPM。

StableDiffusionPipeline中默认的调度器是PNDMScheduler：

from huggingface_hub import login
from diffusers import DiffusionPipeline
import torch
pipeline = DiffusionPipeline.from_pretrained("runwayml/stable-diffusion-v1-5", torch_dtype=torch.float16, use_safetensors=True)
pipeline.to("cuda")
print(pipeline.scheduler)

输出如下：

PNDMScheduler {"_class_name": "PNDMScheduler","_diffusers_version": "0.21.4","beta_end": 0.012,"beta_schedule": "scaled_linear","beta_start": 0.00085,"clip_sample": false,"num_train_timesteps": 1000,"set_alpha_to_one": false,"skip_prk_steps": true,"steps_offset": 1,"timestep_spacing": "leading","trained_betas": null
}

对于不同的Pipeline，我们可以用pipeline.scheduler.compatibles，查看它都有哪些适配的调度器，如StableDiffusionPipeline：

[diffusers.utils.dummy_torch_and_torchsde_objects.DPMSolverSDEScheduler,diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler,diffusers.schedulers.scheduling_lms_discrete.LMSDiscreteScheduler,diffusers.schedulers.scheduling_ddim.DDIMScheduler,diffusers.schedulers.scheduling_ddpm.DDPMScheduler,diffusers.schedulers.scheduling_heun_discrete.HeunDiscreteScheduler,diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler,diffusers.schedulers.scheduling_deis_multistep.DEISMultistepScheduler,diffusers.schedulers.scheduling_pndm.PNDMScheduler,diffusers.schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteScheduler,diffusers.schedulers.scheduling_unipc_multistep.UniPCMultistepScheduler,diffusers.schedulers.scheduling_k_dpm_2_discrete.KDPM2DiscreteScheduler,diffusers.schedulers.scheduling_dpmsolver_singlestep.DPMSolverSinglestepScheduler,diffusers.schedulers.scheduling_k_dpm_2_ancestral_discrete.KDPM2AncestralDiscreteScheduler]

使用pipeline.scheduler.config，我们可用轻松的获得当前pipe调度器的配置参数，这些参数都是Diffusion迭代去噪过程的控制参数（具体原理参考论文），如StableDiffusionPipeline：

FrozenDict([('num_train_timesteps', 1000),('beta_start', 0.00085),('beta_end', 0.012),('beta_schedule', 'scaled_linear'),('trained_betas', None),('skip_prk_steps', True),('set_alpha_to_one', False),('prediction_type', 'epsilon'),('timestep_spacing', 'leading'),('steps_offset', 1),('_use_default_values', ['timestep_spacing', 'prediction_type']),('_class_name', 'PNDMScheduler'),('_diffusers_version', '0.21.4'),('clip_sample', False)])

有了这些参数，我们可以轻松的更换不同的Scheduler，具体选择哪个还得多尝试：

from diffusers import DDIMScheduler
pipeline.scheduler = DDIMScheduler.from_config(pipeline.scheduler.config)from diffusers import LMSDiscreteScheduler
pipeline.scheduler = LMSDiscreteScheduler.from_config(pipeline.scheduler.config)from diffusers import EulerDiscreteScheduler
pipeline.scheduler = EulerDiscreteScheduler.from_config(pipeline.scheduler.config)from diffusers import EulerAncestralDiscreteScheduler
pipeline.scheduler = EulerAncestralDiscreteScheduler.from_config(pipeline.scheduler.config)from diffusers import DPMSolverMultistepScheduler
pipeline.scheduler = DPMSolverMultistepScheduler.from_config(pipeline.scheduler.config)

1.DDPM

接下来我们先以最基础的DDPM为例，分析diffusers库里的对应代码。代码在

diffusers/src/diffusers/schedulers/scheduling_ddpm.py中，以下是核心部分step函数的代码。

step函数完成的操作就是，在去噪过程中：

输入：UNet预测的pred_noise(model_output)、当前timestep(timestep)、当前的latents(sample)。
输出：该timestep去噪后的latents。

    def step(self,model_output: torch.FloatTensor,timestep: int,sample: torch.FloatTensor,generator=None,return_dict: bool = True,) -> Union[DDPMSchedulerOutput, Tuple]:"""Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusionprocess from the learned model outputs (most often the predicted noise).Args:model_output (`torch.FloatTensor`):The direct output from learned diffusion model.timestep (`float`):The current discrete timestep in the diffusion chain.sample (`torch.FloatTensor`):A current instance of a sample created by the diffusion process.generator (`torch.Generator`, *optional*):A random number generator.return_dict (`bool`, *optional*, defaults to `True`):Whether or not to return a [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`.Returns:[`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`:If return_dict is `True`, [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] is returned, otherwise atuple is returned where the first element is the sample tensor."""t = timestepprev_t = self.previous_timestep(t)if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)else:predicted_variance = None# 1. compute alphas_t, betas_talpha_prod_t = self.alphas_cumprod[t]alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.onebeta_prod_t = 1 - alpha_prod_tbeta_prod_t_prev = 1 - alpha_prod_t_prevcurrent_alpha_t = alpha_prod_t / alpha_prod_t_prevcurrent_beta_t = 1 - current_alpha_t# 2. compute predicted original sample from predicted noise also called# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdfif self.config.prediction_type == "epsilon":pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)elif self.config.prediction_type == "sample":pred_original_sample = model_outputelif self.config.prediction_type == "v_prediction":pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_outputelse:raise ValueError(f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"" `v_prediction`  for the DDPMScheduler.")# 3. Clip or threshold "predicted x_0"if self.config.thresholding:pred_original_sample = self._threshold_sample(pred_original_sample)elif self.config.clip_sample:pred_original_sample = pred_original_sample.clamp(-self.config.clip_sample_range, self.config.clip_sample_range)# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t# See formula (7) from https://arxiv.org/pdf/2006.11239.pdfpred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * current_beta_t) / beta_prod_tcurrent_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t# 5. Compute predicted previous sample µ_t# See formula (7) from https://arxiv.org/pdf/2006.11239.pdfpred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample# 6. Add noisevariance = 0if t > 0:device = model_output.devicevariance_noise = randn_tensor(model_output.shape, generator=generator, device=device, dtype=model_output.dtype)if self.variance_type == "fixed_small_log":variance = self._get_variance(t, predicted_variance=predicted_variance) * variance_noiseelif self.variance_type == "learned_range":variance = self._get_variance(t, predicted_variance=predicted_variance)variance = torch.exp(0.5 * variance) * variance_noiseelse:variance = (self._get_variance(t, predicted_variance=predicted_variance) ** 0.5) * variance_noisepred_prev_sample = pred_prev_sample + varianceif not return_dict:return (pred_prev_sample,)return DDPMSchedulerOutput(prev_sample=pred_prev_sample, pred_original_sample=pred_original_sample)

大家从注释可以看出个大概，但是代码里面可能包含了一些额外的if判断导致不是很清楚，所以我把其中最关键的几句骨架提取出来。

alpha_prod_t = self.alphas_cumprod[t]
alpha_prod_t_prev = self.alphas_cumprod[prev_t] if prev_t >= 0 else self.one
beta_prod_t = 1 - alpha_prod_t
beta_prod_t_prev = 1 - alpha_prod_t_prev
current_alpha_t = alpha_prod_t / alpha_prod_t_prev
current_beta_t = 1 - current_alpha_t

以上代码作用是计算当前step的alpha和beta的对应参数，以上变量分别对应了论文中的

在这里插入图片描述

pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)

以上代码根据模型的预测噪声推出原始图像x_{0}，也就是对应论文中公式（15），其中sample就是 $x_{t}$ ，代表当前step的加噪图像，model_output代表模型的预测噪声 $\epsilon$ 。
在这里插入图片描述

pred_original_sample_coeff = (alpha_prod_t_prev ** (0.5) * current_beta_t) / beta_prod_t
current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_tpred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

以上代码计算了 $x_{0}$ 和 $x_{t}$ 的系数，对应公式（7）， $x_{0}$ 代表上一步计算的原始图像， $x_{t}$ 代表当前step的加噪图像，\mu _{t}代表的是分布的均值，对应着代码中的pred_prev_sample。

在这里插入图片描述

pred_prev_sample = pred_prev_sample + variance

最后则是在均值上加上噪声variance。

所以总体而言，整个流程满足公式（6），相当于是在基于 $x_{0}$ 和 $x_{t}$ 基础上 $x_{t-1}$ 的条件概率，而同时也是求一个分布，其中方差（即噪声）完全由step决定，而均值则由初始图像 $x_{0}$ 和当前噪声图像 $x_{t}$ 决定， $x_{0}$ 又通过模型预测得到噪声 $\epsilon$ 计算得到。

在这里插入图片描述

2.DDIM

DDIM就是针对上述DDPM的缺点，对DDPM进行改进的，来提高推理时间，去除了马尔可夫条件的限制，重新推导出逆向扩散方程，在代码scheduling_ddim.py中我们也可以看到对应的修改：
在这里插入图片描述

std_dev_t = eta * variance ** (0.5)
pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon
prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_directionprev_sample = prev_sample + variance

这样我们就可以每次迭代中跨多个step，从而减少推理迭代次数和时间。

3.Euler

当然除了基于DDIM之外还有很多不同原理的采样器，比如Euler，它是基于ODE的比较基础的采样器，以下是Euler在diffusers库scheduling_euler_discrete.py中的核心代码：

pred_original_sample = sample - sigma_hat * model_outputderivative = (sample - pred_original_sample) / sigma_hat
dt = self.sigmas[self.step_index + 1] - sigma_hat
prev_sample = sample + derivative * dt

从代码中可以看出大概的流程：通过对应step的噪声程度预测初始图像，然后通过微分求得对应的梯度方向，然后再向该方向迈进一定步长。