PILD: Physics-Informed Learning via Diffusion

תקציר מקורי באנגליתarXiv:2601.21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and physical constraints through a probabilistic residual formulation with a virtual residual observation sampled from a Laplace distribution. To make this formulation practical under noisy diffusion states, we introduce a Jensen-gap-aware adaptive residual scale, which reduces the bias induced by residual likelihood marginalization. Additionally, we develop a physics-conditional alignment me