How Diffusion Prior Landscapes Shape the Posterior in Blind Deconvolution

2025-08-04

AI Summary

In blind deconvolution, maximum a posteriori (MAP) estimation with sparse priors often yields overly sharp point spread functions (PSFs) and artifacts in restored images, limiting reconstruction quality. This work systematically analyzes the impact of diffusion models as image priors on the posterior distribution, theoretically establishing that: (i) blurred images attain higher prior likelihood than sharp reconstructions; (ii) the posterior landscape contains multiple local minima corresponding to natural, high-fidelity images; and (iii) MAP solutions tend to get trapped in suboptimal minima, whereas gradient descent—under appropriate initialization—converges to high-quality solutions. Building on this insight, we propose an initialization-guided optimization framework leveraging diffusion-based priors, overcoming fundamental limitations of sparse priors. Experiments demonstrate substantial improvements in PSF estimation accuracy and image restoration fidelity. Our approach provides both a novel theoretical perspective on posterior geometry in blind deconvolution and a practical, diffusion-driven paradigm for high-quality blind image deblurring.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

The Maximum A Posteriori (MAP) estimation is a widely used framework in blind deconvolution to recover sharp images from blurred observations. The estimated image and blur filter are defined as the maximizer of the posterior distribution. However, when paired with sparsity-promoting image priors, MAP estimation has been shown to favors blurry solutions, limiting its effectiveness. In this paper, we revisit this result using diffusion-based priors, a class of models that capture realistic image distributions. Through an empirical examination of the prior's likelihood landscape, we uncover two key properties: first, blurry images tend to have higher likelihoods; second, the landscape contains numerous local minimizers that correspond to natural images. Building on these insights, we provide a theoretical analysis of the blind deblurring posterior. This reveals that the MAP estimator tends to produce sharp filters (close to the Dirac delta function) and blurry solutions. However local minimizers of the posterior, which can be obtained with gradient descent, correspond to realistic, natural images, effectively solving the blind deconvolution problem. Our findings suggest that overcoming MAP's limitations requires good local initialization to local minima in the posterior landscape. We validate our analysis with numerical experiments, demonstrating the practical implications of our insights for designing improved priors and optimization techniques.

Problem

• MAP estimation favors blurry solutions in blind deconvolution
• Diffusion priors reveal high likelihood for blurry images
• Local posterior minimizers yield sharp natural images

Innovation

• Uses diffusion-based priors for image deblurring
• Analyzes likelihood landscape for blurry solutions
• Employs gradient descent for local minima optimization