发表机构
Northwestern University（西北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
FlowSGS提出基于分裂吉布斯采样和随机插值的流匹配后验采样方法，用于逆成像，减少网络评估次数并在线性及非线性逆问题上达到最先进性能。
AI 中文摘要
流匹配已成为最先进的生成模型，并被用作即插即用（PnP）先验来解决计算成像中的逆问题。然而，现有的基于流的逆求解器假设线性前向模型和/或在后验采样中做出简化近似。为规避这些问题，我们引入FlowSGS，一种基于流的后验采样方法，使用分裂吉布斯采样（SGS）将后验分解为似然步骤和先验步骤。具体而言，我们使用朗之万动力学从似然步骤中采样，并利用随机插值（SI）框架将预训练的流模型集成到先验步骤中。我们提供了先验步骤的一种形式，该形式使用SI的逆时随机微分方程（SDE），并展示了与先前PnP方法的联系。此外，借助流先验的直线概率路径和一种新颖的逆时SDE时间步校正技术，FlowSGS在先验步骤中所需的网络评估次数少于即插即用扩散采样器。我们的实验在一系列逆问题上展示了最先进的性能。我们首次为基于流的逆求解器提供了非线性逆问题（傅里叶相位恢复）的实验。
英文摘要
Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.
