Hypergraph Generation with Latent Diffusion

Hypergraphs capture high-order interactions that ordinary graphs cannot represent, yet generating realistic ones remains challenging because existing methods often rely on fixed structural assumptions or struggle to model coupled dependencies between nodes and hyperedges. In this work, we propose Janus, a latent diffusion framework that decomposes an observed hypergraph into sub-hypergraphs, learns coupled node and hyperedge latent representations with a dual-view $\beta$-VAE, and generates new structures through paired latent diffusion with cross-view conditioning. The method supports both unconstrained and node-set-constrained generation. We also introduce an evaluation protocol covering micro, meso, and macro scales interactions, structural reconstruction, and high-order similarity measures. Across five real-world datasets and nine baselines, Janus achieves the most stable performance across structural scales, with strong gains in meso-scale and high-order fidelity; in the constrained setting, it consistently obtains the best reconstruction results.