用预训练扩散模型结合蒙特卡洛方法，无须训练即可解贝叶斯逆问题。
Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey
- 通过扭曲扩散过程中的中间分布，引导采样逼近后验分布。
- 利用蒙特卡洛方法从扭曲后的分布中高效采样，实现高精度逆推。
- 适合做贝叶斯推理的科研人员，尤其关注无需重训练的生成建模。
扩散模型能够从复杂分布中生成高度准确的样本，已成为生成建模的基础。近期，它们在作为先验解决贝叶斯逆问题方面展现出巨大潜力。本综述全面概述了当前利用预训练扩散模型结合蒙特卡洛方法求解贝叶斯逆问题的方法，无需额外训练。我们指出，这些方法主要通过扩散过程中中间分布的‘扭曲’机制，引导模拟向后验分布收敛，并描述了不同蒙特卡洛方法如何辅助从这些扭曲分布中采样。
原文摘要 · Abstract (English)
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage \emph{pre-trained} diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a \emph{twisting} mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.
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