FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors

TL;DR

FlowADMM introduces a deterministic operator for flow-based plug-and-play methods, enabling convergence guarantees and improved performance across various inverse problems.

Contribution

It formalizes the deterministic renoise-denoise operator, integrates it into ADMM, and provides convergence analysis for flow-based PnP methods.

Findings

FlowADMM achieves state-of-the-art results on inverse problems.

It requires fewer data consistency evaluations than prior methods.

Convergence guarantees are established under weak Lipschitz conditions.

Abstract

Plug-and-play (PnP) methods for solving inverse problems have recently achieved strong performance by leveraging denoising priors based on powerful generative diffusion and flow models. However, existing diffusion- and flow-based PnP methods typically rely on stochastic renoise-denoise operations, which complicate the analysis of their convergence behavior. In this work, we identify and formalize the deterministic renoise-denoise operator underlying flow-based plug-and-play methods. This perspective reveals that these methods implicitly define a deterministic operator given by the expectation of a denoiser over the latent noise distribution. Building on this insight, we propose FlowADMM, a PnP algorithm that integrates the renoise-denoise operator into the classical alternating direction method of multiplier (ADMM) framework. We establish convergence guarantees for FlowADMM under weak Lipschitz conditions on the underlying flow network, and extend the analysis to non-stationary time schedules. Empirically, FlowADMM achieves state-of-the-art performance among flow-based PnP methods on a range of inverse problems, including denoising, deblurring, super-resolution, and inpainting, while requiring fewer data consistency evaluations than prior approaches.