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.

通过建立基于双曲几何的可解释度度量的几何潜变空间，使用径向和角度几何特性约束的几何潜变过程，HypDiff 框架能有效地捕捉和保留图的拓扑信息，并在各种拓扑结构的图生成中表现出卓越的效果。