PDE-regularized Dynamics-informed Diffusion with Uncertainty-aware Filtering for Long-Horizon Dynamics

arXiv:2604.09058v1 Announce Type: cross Abstract: Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives and fail to capture the underlying dynamics governed by physical laws. In this work, we propose PDYffusion, a dynamics-informe