Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and suboptimal performance. In this paper, we introduce a novel framework that seamlessly incorporates physical priors into diffusion-based generative models to address this limitation. Our approach leverages two categories of priors: 1) distributional priors, such as roto-translational invariance, and 2) physical feasibility priors, including energy and momentum conservation laws and PDE constraints. By embedding these priors into the generative process, our method can efficiently generate physically realistic dynamics, encompassing trajectories and flows. Empirical evaluations demonstrate that our method produces high-quality dynamics across a diverse array of physical phenomena with remarkable robustness, underscoring its potential to advance data-driven studies in AI4Physics. Our contributions signify a substantial advancement in the field of generative modeling, offering a robust solution to generate accurate and physically consistent dynamics.

本研究针对在数据驱动环境中生成符合物理规律的动态难题，提出了一种新框架，将物理先验条件无缝整合进基于扩散的生成模型中。实验证明，该方法能够高效生成高质量的物理动态，具有显著的鲁棒性，推动AI4Physics领域的数据驱动研究。 

在先验条件下生成物理动态