Physics-Constrained Diffusion for Underwater Image Restoration with Spatially Varying Background Light.

Underwater image restoration is challenging due to light absorption and scattering, which cause color distortion, low contrast, and uneven illumination. Existing methods either ignore the underwater imaging process or rely on simplified assumptions, especially treating background light as a spatially uniform component, which limits restoration performance in complex environments. Recent diffusion-based approaches improve restoration quality by exploiting strong image priors, but their physical modeling of background illumination remains insufficient. In this paper, we propose a physics-constrained diffusion method with spatially varying background light for underwater image restoration. The proposed method explicitly models background light by decomposing it into illumination intensity and mixed chromaticity components, and incorporates physical consistency constraints into the diffusion sampling process. A staged optimization strategy is further introduced to progressively optimize physical parameters while keeping the diffusion prior fixed during inference. Experiments on multiple underwater datasets demonstrate consistent improvements in both full-reference and no-reference metrics. The current implementation requires approximately 568 s per 256×256 image and is therefore more suitable for high-quality offline restoration than real-time applications.