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In-loop kernel refinement: Robust blind inverse problems via conditional diffusion and sparse Bayesian learning
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DOI：10.1016/j.neucom.2026.134683.png)
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Abstract
En 中文
Blind image restoration remains a formidable challenge due to the high-dimensional search space and coupled kernel uncertainty. While Diffusion Posterior Sampling (DPS) has shown promise in solving inverse problems, it often suffers from semantic hallucinations and gradient drift when the physical operator is ill-defined. In this paper, we propose an In-Loop Kernel Refinement (ILKR) framework bridging generative manifolds with sparse physical kernels for robust blind restoration. Specifically, we introduce a conditioning mechanism that utilizes Spatial Feature Transform (SFT) layers to anchor the diffusion process within an instance-specific manifold, constraining the solution space. To address kernel uncertainty, a Sparse Bayesian Learning (SBL) optimizer is integrated to dynamically infer the blur kernel via Automatic Relevance Determination (ARD), ensuring realtime calibration of the physical trajectory. Drawing on recent theoretical insights, we reframe this process as a hierarchical Maximum A Posteriori (MAP) optimization, where the generative prior and the sparse physical prior co-evolve to approach a highly favorable trade-off along the perception-fidelity frontier. Experimental results demonstrate that our framework achieves highly competitive performance compared to existing methods, partic ularly delivering superior structural integrity (SSIM) and a well-balanced trade-off along the perception-fidelity frontier in fewer than 20 sampling steps, thereby providing an efficient and mathematically grounded solution for complex unknown degradations.
Keywords:
Sparse Bayesian learning
Diffusion model
Blind image restoration
Condition injector
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