Beyond MMSE: Enhancing PnP Restoration with ProxiMAP

2026-05-12

AI Summary

Traditional plug-and-play (PnP) methods approximate the maximum a posteriori (MAP) solution using MMSE denoisers, often leading to reconstruction distortions; conversely, direct MAP optimization frequently converges to cartoonish results due to score estimation errors. To address these limitations, this work proposes ProxiMAP, a novel iterative MAP approximation framework that dynamically adjusts the noise schedule to align the residual noise at each iteration with the denoiser’s training distribution. This alignment ensures the denoiser operates within its reliable regime and implicitly enforces early stopping. Based on this principle, we design a plug-and-play ProxiMAP module and a computationally efficient hybrid variant. Experiments demonstrate that our approach significantly enhances reconstruction sharpness and quality across diverse inverse problems—including deblurring, inpainting, super-resolution, and phase retrieval—with the hybrid version achieving comparable or superior performance to full substitution schemes at substantially lower computational cost.

Abstract

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable, recent works have sought to close this gap by targeting the MAP with diffusion-model scores. We show this is problematic in practice: learned scores do not match the true ones, so MAP-targeting iterations converge to cartoon-like images rather than realistic ones, and better results are obtained by stopping short of convergence. We turn this observation into a design principle and introduce ProxiMAP, an iterative MAP approximation whose noise schedule keeps the iterate's residual noise matched to the denoiser's training noise. This keeps the denoiser in-distribution where its score is reliable, and yields implicit early stopping that avoids the failure mode above. ProxiMAP is a modular drop-in replacement for MMSE denoisers in standard PnP algorithms and consistently sharpens reconstructions across deblurring, inpainting, super-resolution, and phase retrieval. Building on the same principle, we propose a hybrid variant that applies ProxiMAP only in the late iterations of PnP, where the denoiser is most reliable -- matching or exceeding the full-replacement variant at a fraction of the cost.

Problem

• Plug-and-Play
• MAP estimation
• image restoration
• denoiser mismatch
• score-based diffusion

Innovation

• ProxiMAP
• Plug-and-Play
• MAP estimation
• diffusion models
• denoiser mismatch