GGBall: Graph Generative Model on Poincaré Ball

Tianci Bu, Chuanrui Wang, Hao Ma, Haoren Zheng, Xin Lu, Tailin Wu

Keywords: Hyperbolic Space; Graph Generation; Flow Matching

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

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.
Code is available at: https://github.com/AI4Science-WestlakeU/GGBall.

Primary Area: generative models

Submission Number: 4980