FlowSGS: Improving Flow Priors for Inverse Imaging with Stochastic Interpolants

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 make simplifying approximations in posterior sampling and/or assume linear forward models. In contrast, principled diffusion-based methods exist but are computationally expensive. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) with annealed coupling, and make flow-specific interventions to the prior sampling and annealing steps, theoretically grounded in the Stochastic Interpolants (SI) framework. Using a novel timestep correction and accelerated warm-up with one-step flow models, our method is faster and more accurate than the state of the art across a range of imaging problems. We demonstrate the first use of flow-based samplers for a nonlinear inverse problem (Fourier phase retrieval) and apply one-step flow models to principled Bayesian inverse imaging.