Variational Diffusion Method for Remote Sensing Image Fusion

Image fusion (IF) aims to integrate valuable information from multiple sources, and the fusion of optical image and synthetic aperture radar (SAR) is at the core of remote sensing IF. Despite the remarkable capability of deep learning in IF, it often depends on costly datasets, lacks explicit interpretability, and has an instable training process. Diffusion models (DMs), such as diffusion denoising probabilistic model and its continuous form (i.e., score-based DM), exhibit powerful generative ability and offer novel ideas to address the hurdles above. To this end, it is kernel and challenge to robustly estimate the posterior distribution of ground truth with respect to given measurements. In this letter, we propose a variational diffusion IF method for robust estimation of posterior distribution. First, an optimization model is developed in the framework of variational inference, where the fidelity term comes from traditional optimization fusion model and the regularization term is actually a weighted integral form of the score function matching. Then, a fast numerical algorithm is designed via first-order stochastic optimization, significantly reducing computational complexity. Finally, the proposed method is validated in experiments with WHU-OPT-SAR and SEN1-2 real datasets, and the results show that the proposed method not only outperforms the state-of-the-art methods in terms of fused image quality but also almost has half of computational complexity of existing DM IF methods.