HHGD: Hyperbolic Hypergraph Diffusion for Valid Hypergraph Generation

Hypergraphs provide a natural representation for higher-order relations in social interactions, biological systems, recommender systems, and scientific networks, where pairwise graphs cannot faithfully capture group structure. Generating such data requires learning native node–hyperedge incidence patterns while producing discrete hyperedges with realistic cardinalities and non-degenerate overlaps. We propose HHGD, a hyperbolic latent diffusion framework that jointly represents nodes and hyperedges as tokens in hyperbolic space. HHGD combines an incidence-aware hyperbolic encoder, numerically stable diffusion in the origin tangent space, a curvature-aware hyperbolic score network, and a cardinality-aware Poincar\'e-distance decoder that maps generated tokens to binary incidence matrices. Experiments on synthetic and real-world hypergraph datasets show that HHGD can produce samples with exact uniqueness and novelty, while strict validity varies substantially across datasets and is strongest on several synthetic regimes, attaining the highest displayed mean strict validity on ER, Hypergraph SBM, Tree, and Tags-Math while remaining competitive in matching local and global structural distributions. Comprehensive architecture ablations further show that the hyperbolic latent components provide a coherent inductive bias for higher-order incidence generation, with their strongest benefits appearing in validity and hyperedge-size fidelity, while improvements in global topology remain dataset dependent. These results demonstrate the promise of hyperbolic latent diffusion for valid native hypergraph generation and clarify where its structural benefits are strongest.