PhyDiM: Physics-Guided Diffusion Model for Spatio-Temporal Satellite Image Reconstruction under Sparse Observations

Reconstructing continuous spatio-temporal images from sparse and irregular visual observations is a challenging machine learning problem due to complex spatial dependencies and strong temporal dynamics that must be inferred from a limited number of temporal observations. In this setting, incorporating physical priors is particularly beneficial, as it enables the reconstructed images to respect underlying physical laws and produce more realistic and temporally consistent dynamics. Recent generative approaches, particularly diffusion models, have demonstrated good performance in different reconstruction tasks, but they remain largely data-driven and lack explicit physical structure to guide the generation process. Existing attempts treat physical constraints as external regularization terms in the loss function, which can lead to unstable optimization. In this paper, we introduce PhyDiM, a physics-guided diffusion model that incorporates partial differential equation (PDE) priors directly into the diffusion process. Specifically, we embed the physical constraints directly into both the forward diffusion process and the reverse sampling dynamics. PhyDiM is applied to land surface temperature reconstruction from sparsely sampled satellite observations, where the PDE is instantiated as a heat equation. Experimental results on large-scale and climatically diverse regions covering France, Spain, Germany, Belgium, and the Netherlands demonstrate that PhyDiM consistently outperforms both state-of-the-art reconstruction and diffusion-based methods, particularly at extreme diurnal time steps where existing approaches tend to degrade. Moreover, qualitative analysis further demonstrates that PhyDiM preserves sharper spatial structures and more realistic thermal patterns across diverse conditions.