Hyperbolic Geometric Latent Diffusion Model for Graph Generation

TL;DR

This paper introduces HypDiff, a hyperbolic geometric latent diffusion model that effectively captures and preserves the topological properties of graphs during generation, addressing computational and efficiency issues of prior methods.

Contribution

The paper proposes a novel hyperbolic geometric latent space and anisotropic diffusion process for improved graph generation, enhancing topological preservation and computational efficiency.

Findings

HypDiff outperforms existing models in generating graphs with complex topologies.

The hyperbolic latent space effectively captures non-Euclidean graph structures.

Experimental results show superior topological preservation in generated graphs.

Abstract

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.