  This paper proposes a two-stage framework named ST-PAD for spatio-temporal
fluid dynamics modeling in the field of earth sciences, aiming to achieve
high-precision simulation and prediction of fluid dynamics through
spatio-temporal physics awareness and parameter diffusion guidance. In the
upstream stage, we design a vector quantization reconstruction module with
temporal evolution characteristics, ensuring balanced and resilient parameter
distribution by introducing general physical constraints. In the downstream
stage, a diffusion probability network involving parameters is utilized to
generate high-quality future states of fluids, while enhancing the model's
generalization ability by perceiving parameters in various physical setups.
Extensive experiments on multiple benchmark datasets have verified the
effectiveness and robustness of the ST-PAD framework, which showcase that
ST-PAD outperforms current mainstream models in fluid dynamics modeling and
prediction, especially in effectively capturing local representations and
maintaining significant advantages in OOD generations.
