Discovering Symmetry Groups with Flow Matching

The article introduces LieFlow, a novel framework for discovering symmetry groups by reframing the problem as a distribution learning task on Lie groups. LieFlow operates directly in group space to model a symmetry distribution, enabling it to identify both continuous and discrete symmetries without relying on a fixed Lie algebra basis. Experimental results demonstrate that LieFlow significantly outperforms the state-of-the-art baseline, LieGAN, in accurately discovering symmetries in synthetic point clouds and real-world datasets, which is crucial for enhancing performance and sample efficiency in machine learning applications.