PnP-CF: A Consensus Flow-Matching Solver for General Inverse Problems

Plug-and-Play (PnP) methods using continuous-time deep generative models as learned data distribution priors enable synthesizing high-quality solutions of model-based inverse problems. The quality of the solutions depends critically on the interplay and consensus between the inverse problem solver and the generative model sampler. We propose a new PnP-CF (Consensus Flow) method, a PnP algorithm with flow-matching denoiser using (i) ADMM-like dual variable updates and (ii) time-adaptive pullback onto the intermediate flow probability path combining a stochastic and a deterministic component. We discuss how these two features stabilize the algorithm and promote consensus, and demonstrate on a set of experiments that our PnP-CF not only solves standard linear inverse problems with quality at least comparable to the state-of-the-art baselines, but also gracefully extends to nonlinear inverse problems for which the existing methods produce unsatisfactory results or fail completely.