Beyond MMSE: Enhancing PnP Restoration with ProxiMAP
Quick Take
ProxiMAP enhances PnP restoration by aligning noise schedules with denoiser training, improving image quality.
Key Points
- ProxiMAP targets MAP with reliable noise matching.
- Improves results in deblurring, inpainting, and super-resolution.
- Hybrid variant offers cost-effective performance enhancements.
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~2 min readAbstract: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.
| Subjects: | Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.16396 [cs.CV] |
| (or arXiv:2605.16396v1 [cs.CV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16396 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kenta Vert [view email]
[v1]
Tue, 12 May 2026 15:54:26 UTC (16,650 KB)
— Originally published at arxiv.org
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