用分层对称策略高效生成稳定晶体结构，解决材料设计难题。

Discovering new solid-state materials requires rapidly exploring the vast space of crystal structures and locating stable regions. Generating stable materials with desired properties and compositions is extremely difficult as we search for very small isolated pockets in the exponentially many possibilities, considering elements from the periodic table and their 3D arrangements in crystal lattices. Materials discovery necessitates both optimized solution structures and diversity in the generated material structures. Existing methods struggle to explore large material spaces and generate diverse samples with desired properties and requirements. We propose the Symmetry-aware Hierarchical Architecture for Flow-based Traversal (SHAFT), a novel generative model employing a hierarchical exploration strategy to efficiently exploit the symmetry of the materials space to generate crystal structures given desired properties. In particular, our model decomposes the exponentially large materials space into a hierarchy of subspaces consisting of symmetric space groups, lattice parameters, and atoms. We demonstrate that SHAFT significantly outperforms state-of-the-art iterative generative methods, such as Generative Flow Networks (GFlowNets) and Crystal Diffusion Variational AutoEncoders (CDVAE), in crystal structure generation tasks, achieving higher validity, diversity, and stability of generated structures optimized for target properties and requirements.