Title: GGBall: Graph Generative Model on Poincaré Ball
Primary area: generative models
Keywords: Hyperbolic Space; Graph Generation; Flow Matching

Abstract: Generating graphs with hierarchical structures remains a fundamental challenge
due to the limitations of Euclidean geometry in capturing exponential complexity.
Here we introduce GGBall, a novel hyperbolic framework for graph generation
that integrates geometric inductive biases with modern generative paradigms. GGBall combines a Hyperbolic Vector-Quantized Autoencoder (HVQVAE) with a
Riemannian flow matching prior defined via closed-form geodesics. This design
enables flow-based priors to model complex latent distributions, while vector quantization helps preserve the curvature-aware structure of the hyperbolic space. We
further develop a suite of hyperbolic GNN and Transformer layers that operate
entirely within the manifold, ensuring stability and scalability. Empirically, GGBall
establishes a new state-of-the-art across diverse benchmarks. On hierarchical graph
datasets, it reduces the average generation error by up to 18% compared to the
strongest baselines. These results highlight the potential of hyperbolic geometry
as a powerful foundation for the generative modeling of complex, structured, and
hierarchical data domains.

TL;DR: The first graph generation framework built upon the Poincaré Ball model of hyperbolic space.