做图像逆问题或扩散模型后验采样的研究者，这篇论文直接戳中了现有方法“好用但说不清为什么失败”的痛点——有限样本视角给出了可落地的诊断工具，建议点开看看你的采样器是否也在犯这些错误。
本文从有限样本视角系统分析了扩散模型在后验采样中的失败机制。研究发现，现有方法在中间时间步对似然函数进行近似时，会系统性地高估或低估后验分布的扩散程度，导致对早期停止时间敏感、后验模式权重不准确以及产生幻觉（包括先验中不存在但后验中出现的模式，以及似然中不受先验支持的模式）。这些错误无需非线性测量模型或多模态后验，仅由多模态先验和中间采样时的不准确后验扩散即可引发。作者提出的有限样本后验采样方法可兼容任何似然近似和正向模型，作为诊断工具评估现有及未来后验采样器的准确性和失败模式。
When, why, and how do diffusion posterior samplers fail? A finite-sample lens
Diffusion models have excellent capacity to model complex distributions of natural data, which has made them a popular and effective choice for posterior sampling in imaging inverse problems. Existing methods can incorporate any measurement model at inference time but must use an inexact approximation for the likelihood at intermediate timesteps for computational tractability. Although these approximations can often work well empirically, their downstream effect on the sampled posterior is poorly understood and can result in unexplained failures. To understand when, why, and how these likelihood approximations propagate to erroneous posterior distributions, we introduce a finite-sample perspective on posterior sampling that approximates the posterior to arbitrary precision as training set size tends towards infinity, for any forward model and prior distribution. Using this finite-sample lens, we observe that popular posterior sampling approximations tend to under- or over-estimate the spread of the posterior at intermediate timesteps, causing downstream consequences including sensitivity to early stopping time, inaccurate relative weighting of posterior modes, and hallucination, both of prior modes that are not in the posterior and likelihood modes that are not supported by the prior. Moreover, we find that the cause of these posterior errors requires neither a nonlinear measurement model nor a multimodal posterior, but can arise solely due to a multimodal prior and inaccurate posterior spread at intermediate sampling times. Our finite-sample posterior sampling approach is agnostic to the type of likelihood approximation and the type of (linear or nonlinear) forward model, and can thus serve as a drop-in diagnostic to evaluate the accuracy and failure modes of existing and future posterior samplers.