We present FMPlug, a novel plug-in framework that enhances foundation flow-matching (FM) priors for solving ill-posed inverse problems. Unlike traditional approaches that rely on domain-specific or untrained priors, FMPlug smartly leverages two simple but powerful insights: the similarity between observed and desired objects and the Gaussianity of generative flows. By introducing a time-adaptive warm-up strategy and sharp Gaussianity regularization, FMPlug unlocks the true potential of domain-agnostic foundation models. Our method beats state-of-the-art methods that use foundation FM priors by significant margins, on image super-resolution and Gaussian deblurring.

Foundation flow-matching (FM) models promise a universal prior for solving inverse problems (IPs), yet today they trail behind domain-specific or even untrained priors. How can we unlock their potential? We introduce FMPlug, a plug-in framework that redefines how foundation FMs are used in IPs. FMPlug combines an instance-guided, time-dependent warm-start strategy with a sharp Gaussianity regularization, adding problem-specific guidance while preserving the Gaussian structures. This leads to a significant performance boost across image restoration and scientific IPs. Our results point to a path for making foundation FM models practical, reusable priors for IP solving.

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.