[2603.10281] Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework

Computer Science > Machine Learning arXiv:2603.10281 (cs) [Submitted on 10 Mar 2026 (v1), last revised 27 Mar 2026 (this version, v2)] Title:Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework Authors:Rajesh Shrestha, Xiao Fu View a PDF of the paper titled Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework, by Rajesh Shrestha and 1 other authors View PDF HTML (experimental) Abstract:While score-based generative models have emerged as powerful priors for solving inverse problems, directly integrating them into optimization algorithms such as ADMM remains nontrivial. Two central challenges arise: i) the mismatch between the noisy data manifolds used to train the score functions and the geometry of ADMM iterates, especially due to the influence of dual variables, and ii) the lack of convergence understanding when ADMM is equipped with score-based denoisers. To address the manifold mismatch issue, we propose ADMM plug-and-play (ADMM-PnP) with the AC-DC denoiser, a new framework that embeds a three-stage denoiser into ADMM: (1) auto-correction (AC) via additive Gaussian noise, (2) directional correction (DC) using conditional Langevin dynamics, and (3) score-based denoising. In terms of convergence, we establish two results: first, under proper denoiser parameters, each ADMM iteration is a weakly nonexpansive operator, ensuring high-probability fixed-point $\textit{ball convergence}$ using a constant step size; second, under more r...