Hyperbolic Geometric Latent Diffusion Model for Graph Generation

Xingcheng Fu, Yisen Gao, Yuecen Wei, Qingyun Sun, Hao Peng, Jianxin Li, Xianxian Li
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:14102-14124, 2024.

Abstract

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of it to graph generation. The 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-fu24c, title = {Hyperbolic Geometric Latent Diffusion Model for Graph Generation}, author = {Fu, Xingcheng and Gao, Yisen and Wei, Yuecen and Sun, Qingyun and Peng, Hao and Li, Jianxin and Li, Xianxian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {14102--14124}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/fu24c/fu24c.pdf}, url = {https://proceedings.mlr.press/v235/fu24c.html}, abstract = {Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of it to graph generation. The 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.} }
Endnote
%0 Conference Paper %T Hyperbolic Geometric Latent Diffusion Model for Graph Generation %A Xingcheng Fu %A Yisen Gao %A Yuecen Wei %A Qingyun Sun %A Hao Peng %A Jianxin Li %A Xianxian Li %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-fu24c %I PMLR %P 14102--14124 %U https://proceedings.mlr.press/v235/fu24c.html %V 235 %X Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of it to graph generation. The 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.
APA
Fu, X., Gao, Y., Wei, Y., Sun, Q., Peng, H., Li, J. & Li, X.. (2024). Hyperbolic Geometric Latent Diffusion Model for Graph Generation. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:14102-14124 Available from https://proceedings.mlr.press/v235/fu24c.html.

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