郑州网站建设时一定需要注意的六点,深圳龙华区龙华街道高坳新村,社保网站上20号做的新增,旅游网站开发答辩ppt随机微分方程的分数扩散模型#xff08;Score-Based Generative Modeling through Stochastic Differential Equations#xff09; 基于分数的扩散模型#xff0c;是估计数据分布梯度的方法#xff0c;可以在不需要对抗训练的基础上#xff0c;生成与GAN一样高质量的图片。…随机微分方程的分数扩散模型Score-Based Generative Modeling through Stochastic Differential Equations 基于分数的扩散模型是估计数据分布梯度的方法可以在不需要对抗训练的基础上生成与GAN一样高质量的图片。来源于文章Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-Based Generative Modeling through Stochastic Differential Equations. Internation Conference on Learning Representations, 2021
score-based diffusion是diffusion模型大火之后又一个里程碑式的工作将扩散模型和分数生成模型进行了统一。原始的扩散模型也有缺点它的采样速度慢通常需要数千个评估步骤才能抽取一个样本。而 score-based 的扩散模型可以在较短的时间内完成采样。 网络上有很多关于score-based diffusion原理介绍应用案例等还有文章解读大家可以参考。但是提供代码简介的很少为此这里提供了score-based diffusion 模型的简单的可运行的代码示例。 1. 定义time-dependent score-based模型 导入相关模块
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as npimport torch
import functools
from torch.optim import Adam
from torch.utils.data import DataLoader
import torchvision.transforms as transforms
from torchvision.datasets import MNIST
import tqdm 1.1 将时间t嵌入的投影层
其实并没有投影层的说法这里是为了描述将时间t time step随机初始化采样权重然后使用[sin(2πωt);cos(2πωt)]生成相应的高斯随机特征向量的过程。注意里面的参数是不可训练的。 class GaussianFourierProjection(nn.Module):Gaussian random features for encoding time steps. def __init__(self, embed_dim, scale30.):super().__init__()# 在初始化期间随机采样权重。 这些权重是固定的 # 在优化期间并且不可训练self.W nn.Parameter(torch.randn(embed_dim // 2) * scale, requires_gradFalse)def forward(self, x):x_proj x[:, None] * self.W[None, :] * 2 * np.pireturn torch.cat([torch.sin(x_proj), torch.cos(x_proj)], dim-1)
将时间t嵌入的投影层的出现是因为score-based的扩散模型和正常的扩散模型的训练过程不一样。score-based的扩散模型在训练过程中神经网络接受带有随机噪音的 x 然后随机的时间信息 t 添加x中然后利用x 和 t 作为输入计算模型损失。 维度转换全连接层
class Dense(nn.Module):A fully connected layer that reshapes outputs to feature maps.def __init__(self, input_dim, output_dim):super().__init__()self.dense nn.Linear(input_dim, output_dim)def forward(self, x):return self.dense(x)[..., None, None] 1.2 时间依赖基于分数的Unet模型
time-dependent score-based model 时间依赖打分相关的Unet模型froward函数中输入除了x还有时间t. 时间t经过GaussianFourierProjection嵌入后融合到模型中然后输出marginal_prob_std正则化的结果。
class ScoreNet(nn.Module):初始化一个依赖时间的基于分数的Unet网络.def __init__(self, marginal_prob_std, channels[32, 64, 128, 256], embed_dim256):.Args:marginal_prob_std: 输入时间 t 并给出扰动核的标准差的函数 p_{0t}(x(t) | x(0)).channels: 各分辨率特征图的通道数.embed_dim: 高斯随机特征嵌入的维数与1.1中GaussianFourierProjection相同.super().__init__()# 时间t的高斯随机特征嵌入层self.embed nn.Sequential(GaussianFourierProjection(embed_dimembed_dim),nn.Linear(embed_dim, embed_dim))# Encoding layers where the resolution decreasesself.conv1 nn.Conv2d(1, channels[0], 3, stride1, biasFalse)self.dense1 Dense(embed_dim, channels[0])self.gnorm1 nn.GroupNorm(4, num_channelschannels[0])self.conv2 nn.Conv2d(channels[0], channels[1], 3, stride2, biasFalse)self.dense2 Dense(embed_dim, channels[1])self.gnorm2 nn.GroupNorm(32, num_channelschannels[1])self.conv3 nn.Conv2d(channels[1], channels[2], 3, stride2, biasFalse)self.dense3 Dense(embed_dim, channels[2])self.gnorm3 nn.GroupNorm(32, num_channelschannels[2])self.conv4 nn.Conv2d(channels[2], channels[3], 3, stride2, biasFalse)self.dense4 Dense(embed_dim, channels[3])self.gnorm4 nn.GroupNorm(32, num_channelschannels[3]) # 分辨率增加的解码层self.tconv4 nn.ConvTranspose2d(channels[3], channels[2], 3, stride2, biasFalse)self.dense5 Dense(embed_dim, channels[2])self.tgnorm4 nn.GroupNorm(32, num_channelschannels[2])self.tconv3 nn.ConvTranspose2d(channels[2] channels[2], channels[1], 3, stride2, biasFalse, output_padding1) self.dense6 Dense(embed_dim, channels[1])self.tgnorm3 nn.GroupNorm(32, num_channelschannels[1])self.tconv2 nn.ConvTranspose2d(channels[1] channels[1], channels[0], 3, stride2, biasFalse, output_padding1) self.dense7 Dense(embed_dim, channels[0])self.tgnorm2 nn.GroupNorm(32, num_channelschannels[0])self.tconv1 nn.ConvTranspose2d(channels[0] channels[0], 1, 3, stride1)# Swish 激活函数self.act lambda x: x * torch.sigmoid(x)self.marginal_prob_std marginal_prob_stddef forward(self, x, t): # 0 embed self.act(self.embed(t)) # Encoding pathh1 self.conv1(x) ## 合并来自 t 的信息h1 self.dense1(embed)## 组标准化h1 self.gnorm1(h1)h1 self.act(h1)h2 self.conv2(h1)h2 self.dense2(embed)h2 self.gnorm2(h2)h2 self.act(h2)h3 self.conv3(h2)h3 self.dense3(embed)h3 self.gnorm3(h3)h3 self.act(h3)h4 self.conv4(h3)h4 self.dense4(embed)h4 self.gnorm4(h4)h4 self.act(h4)# Decoding pathh self.tconv4(h4)## 从编码路径跳过连接h self.dense5(embed)h self.tgnorm4(h)h self.act(h)h self.tconv3(torch.cat([h, h3], dim1))h self.dense6(embed)h self.tgnorm3(h)h self.act(h)h self.tconv2(torch.cat([h, h2], dim1))h self.dense7(embed)h self.tgnorm2(h)h self.act(h)h self.tconv1(torch.cat([h, h1], dim1))# Normalize output 正则化输出h h / self.marginal_prob_std(t)[:, None, None, None]return h 2. 设置SDE
SDE用于将P_0扰动到P_T 其中包含两个重要函数之前提到的marginal_prob_std和扩散系数diffusion_coeff marginal_prob_std计算 p_{0t}(x(t) | x(0)) 的平均值和标准差 diffusion_coeff计算SDE的扩散系数.
device cuda #param [cuda, cpu] {type:string}def marginal_prob_std(t, sigma):计算p_{0t}(x(t) | x(0))的平均值和标准差.Args: t: A vector of time steps.sigma: The $\sigma$ in our SDE. Returns:标准差. t torch.tensor(t, devicedevice)return torch.sqrt((sigma**(2 * t) - 1.) / 2. / np.log(sigma))def diffusion_coeff(t, sigma):计算SDE的扩散系数.Args:t: A vector of time steps.sigma: The $\sigma$ in our SDE.Returns:扩散系数向量.return torch.tensor(sigma**t, devicedevice)sigma 25.0 #param {type:number}
marginal_prob_std_fn functools.partial(marginal_prob_std, sigmasigma)
diffusion_coeff_fn functools.partial(diffusion_coeff, sigmasigma)
