Beyond MMSE: Enhancing PnP Restoration with ProxiMAP
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911690300325888 |
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| author | Vert, Kenta Meanti, Giacomo Pesme, Scott Arbel, Michael Mairal, Julien |
| author_facet | Vert, Kenta Meanti, Giacomo Pesme, Scott Arbel, Michael Mairal, Julien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond MMSE: Enhancing PnP Restoration with ProxiMAP Vert, Kenta Meanti, Giacomo Pesme, Scott Arbel, Michael Mairal, Julien Computer Vision and Pattern Recognition Machine Learning 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. |
| title | Beyond MMSE: Enhancing PnP Restoration with ProxiMAP |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2605.16396 |