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

2026-05-08

AI Summary

This work addresses the lack of convergence guarantees in existing plug-and-play (PnP) methods based on flow models, which rely on stochastic renoising–denoising operations that hinder theoretical analysis. For the first time, we formalize the implicit deterministic renoising–denoising operator within flow models and integrate it into an Alternating Direction Method of Multipliers (ADMM) framework, yielding the FlowADMM algorithm with provable convergence. Under mild Lipschitz conditions, our method accommodates non-stationary time schedules and achieves state-of-the-art performance among flow-based PnP approaches across diverse inverse problems—including denoising, deblurring, super-resolution, and image inpainting—while significantly reducing the number of data-consistency evaluations required.

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.

Problem

• inverse problems
• plug-and-play methods
• flow-based models
• convergence analysis
• denoising priors

Innovation

• Plug-and-play
• Flow-based generative models
• ADMM
• Deterministic renoise-denoise operator
• Convergence guarantees