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.

翻译：在数据驱动背景下生成物理可行的动力学具有挑战性，尤其是在需要遵循以特定方程或公式表达的物理先验时。现有方法往往忽视物理先验的整合，导致违反基本物理定律且性能欠佳。本文提出一种新颖框架，将物理先验无缝融入基于扩散的生成模型以解决此局限。我们的方法利用两类先验：1）分布先验，如旋转平移不变性；2）物理可行性先验，包括能量与动量守恒定律以及偏微分方程约束。通过将这些先验嵌入生成过程，本方法能高效生成物理真实的动力学，涵盖轨迹与流场。实证评估表明，本方法能在多种物理现象中生成高质量动力学，并展现出卓越的鲁棒性，凸显其在AI4Physics数据驱动研究中的推进潜力。我们的贡献标志着生成建模领域的重大进展，为生成精确且物理一致的动力学提供了稳健解决方案。