<p>Infrared and visible image fusion aims to generate fused images that maintain the advantages of each source such as temperature information and detailed textures. This paper presents Bayesian Model-based Fusion-Net, a novel approach for infrared and visible image fusion. By formulating image fusion as an inverse problem within a hierarchical Bayesian framework, our method leverages physical priors and data-driven techniques to enhance model interpretability and transferability. Compared to traditional and deep learning-based fusion methods, the proposed Bayesian Model-based Fusion-Net achieves promising performance with significantly reduced computational complexity (0.07G FLOPs). Extensive experiments on multiple datasets, including industrial public dataset, demonstrate the effectiveness of the proposed method in preserving texture details, maintaining structural integrity, and enhancing feature clarity. Furthermore, our approach exhibits robustness when trained with limited data, maintaining consistent performance even when using only 10% of the training dataset. These characteristics make the proposed Bayesian Fusion-Net particularly suitable for industrial monitoring applications where computational resources and the amount of training dataset are limited.</p>