扩散模型做贝叶斯逆问题后验采样：按在线-离线开销划分的方法综述
Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
用扩散模型做逆问题的朋友可以看这篇综述，按离线/在线开销把 likelihood guidance、SMC 校正等方法梳理得很清楚，还列了加速方向。
这是一篇选择性综述，讨论如何用 score-based 扩散模型加速贝叶斯逆问题中的后验采样。核心难点是：仅凭先验 score 无法直接得到加噪后验的 score，需要额外处理。文中梳理了 likelihood guidance、谱方法与投影方法、sequential Monte Carlo 校正、amortized 条件训练等四类主要方案。综述按离线准备与在线推理之间的开销划分方式组织这些方法，比较各自的假设、优势和局限，重点放在计算加速上。
Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
Bayesian inverse problems require both informative prior models and computationally feasible posterior inference. Score-based diffusion models provide expressive learned priors, but their use for inversion introduces a conditioning problem: the score of a noised posterior is generally unavailable from a prior score alone. This selective survey reviews the principal approaches to that problem, including likelihood guidance, spectral and projection methods, sequential Monte Carlo corrections, and amortized conditional training. We organize methods by how they split cost between offline preparation and online inference, and compare their assumptions, advantages and limitations, with emphasis on computational speedups. Some ongoing directions and open questions are gathered at the end.