  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.
