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

2026-03-10

AI Summary

This work addresses the challenges of manifold mismatch and lack of convergence guarantees when directly embedding score-based generative models into optimization algorithms such as ADMM. To resolve these issues, the authors propose the ADMM-PnP framework, which for the first time enables a Plug-and-Play method within ADMM with provable convergence. The framework introduces an AC-DC three-stage denoising mechanism that integrates additive Gaussian noise with self-correction (AC), direction-corrected conditional Langevin dynamics (DC), and score-based denoising, while combining constant and adaptive stepsize strategies. This design effectively mitigates manifold mismatch and simultaneously ensures geometric consistency and algorithmic convergence. Experiments demonstrate that the proposed method consistently achieves superior solution quality over existing baselines across various inverse problems, empirically validating its theoretical convergence guarantees.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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 relaxed conditions, the AC-DC denoiser is a bounded denoiser, which leads to convergence under an adaptive step size schedule. Experiments on a range of inverse problems demonstrate that our method consistently improves solution quality over a variety of baselines.

Problem

• score-based denoisers
• ADMM
• manifold mismatch
• convergence
• inverse problems

Innovation

• score-based denoising
• ADMM
• plug-and-play
• convergence analysis
• manifold correction