Beyond MMSE: Enhancing PnP Restoration with ProxiMAP

2026-05-19 · Source: cs.CV updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computer Vision · Depth: Expert, extended

Summary

ProxiMAP is a novel iterative algorithm designed to enhance Plug-and-Play (PnP) image restoration methods by addressing the mismatch between the intractable maximum a posteriori (MAP) denoiser and the commonly used minimum mean squared error (MMSE) denoiser. Traditional MAP-targeting approaches with learned diffusion model scores often converge to "cartoon-like" images due to inexact scores. ProxiMAP mitigates this by employing a noise schedule that keeps the iterate's residual noise matched to the denoiser's training noise, ensuring the denoiser operates in-distribution and providing implicit early stopping. This modular algorithm, a drop-in replacement for MMSE denoisers, consistently sharpens reconstructions across tasks like deblurring, inpainting, super-resolution, and phase retrieval. A hybrid variant, applying ProxiMAP only in late PnP iterations, achieves comparable or superior results at a significantly reduced computational cost, improving the perception-distortion trade-off for existing PnP frameworks.

Key takeaway

Research Scientists working on image restoration with Plug-and-Play methods should consider integrating ProxiMAP, particularly its Fast ProxiMAP hybrid variant. This approach offers sharper, more perceptually accurate reconstructions by addressing the limitations of learned scores in MAP estimation, often at a fraction of the computational cost of full ProxiMAP replacement. You can achieve significant LPIPS improvements across various inverse problems without needing to retrain underlying diffusion models.

Key insights

ProxiMAP enhances PnP image restoration by aligning denoiser noise schedules to prevent "cartoon-like" artifacts from inexact learned scores.

Principles

• Learned scores can displace MAP modes from true data distribution.
• Denoisers are reliable only on in-distribution noise statistics.
• Implicit early stopping prevents drift into failure regimes.

Method

ProxiMAP iteratively approximates MAP by matching the iterate's residual noise level to the denoiser's training noise level, using a specific step-size and noise schedule derived from smoothed gradient descent, and returning the final MMSE estimate.

In practice

• Integrate ProxiMAP as a drop-in replacement for MMSE denoisers.
• Use the hybrid variant for cost-effective performance.
• Tune final variance $\sigma_K$ for optimal results.

Topics

• Plug-and-Play Restoration
• MAP Estimation
• Diffusion Models
• Image Inverse Problems
• ProxiMAP Algorithm

Code references

• LeviBorodenko/motionblur

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Computer Vision Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.CV updates on arXiv.org.