Beyond Pairwise Interactions: Equivariant Hypergraph Diffusion for Crystal Structure Prediction

Crystal Structure Prediction (CSP) remains a fundamental challenge with significant implications for materials discovery and the advancement of various scientific disciplines. Recent advances have demonstrated that generative models, particularly diffusion models, are especially promising for CSP. However, traditional graph-based representations, where atomic bonds are modeled as pairwise graph edges, fail to capture the intricate high-order interactions essential for accurately describing crystal structures. To address this limitation, we propose leveraging hypergraphs to represent crystal structures, enabling more expressive modeling of multi-way atomic interactions. Hypergraphs naturally encode complex high-order relationships and respect key symmetries -- such as permutation and periodic translation invariance -- that are crucial for characterizing crystalline materials. Building on this representation, we propose the \textbf{E}quivariant \textbf{H}ypergraph \textbf{Diff}usion Model (\textbf{EH-Diff}), a generative framework designed to exploit the symmetry-preserving properties of hypergraphs. EH-Diff provides an efficient and accurate method for predicting crystal structures, with rigorous theoretical guarantees on invariance preservation. Empirically, we conduct extensive experiments on four benchmark datasets, and the results demonstrate that EH-Diff outperforms state-of-the-art CSP methods even with a single diffusion sample.