Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework
arXiv:2603.10281v1 Announce Type: new 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, e
arXiv:2603.10281v1 Announce Type: new 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.
Executive Summary
The article 'Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework' proposes a novel framework for integrating score-based generative models into optimization algorithms like ADMM. The framework, called ADMM plug-and-play (ADMM-PnP), overcomes the challenges of manifold mismatch and convergence understanding by incorporating a three-stage denoiser. Experiments demonstrate improved solution quality over various baselines. While the framework offers a promising solution, its applicability is limited to specific inverse problems. The authors' contributions to convergence understanding and the development of a bounded denoiser are notable. However, further investigation into the theoretical underpinnings of the proposed framework is necessary to ensure its robustness and scalability.
Key Points
- ▸ Proposes a novel framework for integrating score-based generative models into ADMM
- ▸ Overcomes manifold mismatch and convergence understanding challenges
- ▸ Incorporates a three-stage denoiser for improved solution quality
Merits
Strength in Convergence Understanding
The authors establish two convergence results, ensuring high-probability fixed-point ball convergence and bounded denoiser convergence under specific conditions.
Improved Solution Quality
Experiments demonstrate that the proposed framework consistently improves solution quality over various baselines.
Demerits
Limited Applicability
The framework's applicability is limited to specific inverse problems, restricting its broader utility.
Theoretical Underpinnings
Further investigation into the theoretical underpinnings of the proposed framework is necessary to ensure its robustness and scalability.
Expert Commentary
The article presents a significant contribution to the field of optimization and machine learning, showcasing the potential of score-based generative models in solving inverse problems. However, the proposed framework's limitations and the need for further theoretical investigation underscore the importance of continued research in this area. As the field continues to evolve, it is essential to balance the pursuit of improved solution quality with the need for robust and scalable frameworks that can be applied to a wide range of problems.
Recommendations
- ✓ Further investigation into the theoretical underpinnings of the proposed framework is necessary to ensure its robustness and scalability.
- ✓ Exploring the application of the proposed framework to a broader range of inverse problems and fields can help to establish its broader utility and impact.