中国大学数据科学学院：2024年生成型人工智能扩散模型概述（英文版）（56页）.pdf

1、An overview of diffusion modelsfor generative artificial intelligenceDavide Gallon1,Arnulf Jentzen2,3,and Philippe von Wurstemberger4,51Applied Mathematics:Institute for Analysisand Numerics,University of M unster,Germany,e-mail:davide.gallonuni-muenster.de2School of Data Science and Shenzhen Resear

2、ch Institute ofBig Data,The Chinese University of Hong Kong,Shenzhen(CUHK-Shenzhen),China,e-mail:3Applied Mathematics:Institute for Analysis and Numerics,University of M unster,Germany,e-mail:ajentzenuni-muenster.de4Risklab,Department of Mathematics,ETH Zurich,Switzerland,e-mail:philippe.vonwurstemb

3、ergermath.ethz.ch5School of Data Science,The Chinese University ofHong Kong,Shenzhen(CUHK-Shenzhen),China,e-mail:December 3,2024AbstractThis article provides a mathematically rigorous introduction to denoising diffusion prob-abilistic models(DDPMs),sometimes also referred to as diffusion probabilist

4、ic models ordiffusion models,for generative artificial intelligence.We provide a detailed basic mathe-matical framework for DDPMs and explain the main ideas behind training and generationprocedures.In this overview article we also review selected extensions and improvementsof the basic framework fro

5、m the literature such as improved DDPMs,denoising diffusionimplicit models,classifier-free diffusion guidance models,and latent diffusion models.Contents1Introduction32Denoising diffusion probabilistic models(DDPMs)42.1General framework for DDPMs.41arXiv:2412.01371v1 cs.LG 2 Dec 20242.2Training obje

6、ctive in DDPMs.82.3A first simplified DDPM generative method.123DDPMs with Gaussian noise143.1Properties of Gaussian distributions.143.1.1On Gaussian transition kernels.153.1.2Explicit constructions for Gaussian transition kernels.153.1.3Bayes rule for Gaussian distributions.163.1.4KL divergence bet