Hyperbolic Geometric Latent Diffusion Model for Graph Generation
- URL: http://arxiv.org/abs/2405.03188v1
- Date: Mon, 6 May 2024 06:28:44 GMT
- Title: Hyperbolic Geometric Latent Diffusion Model for Graph Generation
- Authors: Xingcheng Fu, Yisen Gao, Yuecen Wei, Qingyun Sun, Hao Peng, Jianxin Li, Xianxian Li,
- Abstract summary: 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.
In this paper, 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.
- Score: 27.567428462212455
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
Related papers
- Geometric Trajectory Diffusion Models [58.853975433383326]
Generative models have shown great promise in generating 3D geometric systems.
Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature.
We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
arXiv Detail & Related papers (2024-10-16T20:36:41Z) - Advancing Graph Generation through Beta Diffusion [49.49740940068255]
Graph Beta Diffusion (GBD) is a generative model specifically designed to handle the diverse nature of graph data.
We propose a modulation technique that enhances the realism of generated graphs by stabilizing critical graph topology.
arXiv Detail & Related papers (2024-06-13T17:42:57Z) - Advective Diffusion Transformers for Topological Generalization in Graph
Learning [69.2894350228753]
We show how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies.
We propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations.
arXiv Detail & Related papers (2023-10-10T08:40:47Z) - Hyperbolic Graph Diffusion Model [24.049660417511074]
We propose a novel graph generation method called, Hyperbolic Graph Diffusion Model (HGDM)
HGDM consists of an auto-encoder to encode nodes into successive hyperbolic embeddings, and a DM that operates in the hyperbolic latent space.
Experiments show that HGDM achieves better performance in generic graph and molecule generation benchmarks, with a $48%$ improvement in the quality of graph generation with highly hierarchical structures.
arXiv Detail & Related papers (2023-06-13T08:22:18Z) - Projections of Model Spaces for Latent Graph Inference [18.219577154655006]
Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias.
Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.
arXiv Detail & Related papers (2023-03-21T11:20:22Z) - Graph Generation with Diffusion Mixture [57.78958552860948]
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures.
We propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process.
arXiv Detail & Related papers (2023-02-07T17:07:46Z) - Generative Diffusion Models on Graphs: Methods and Applications [50.44334458963234]
Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks.
Graph generation is a crucial computational task on graphs with numerous real-world applications.
arXiv Detail & Related papers (2023-02-06T06:58:17Z) - Conditional Diffusion Based on Discrete Graph Structures for Molecular
Graph Generation [32.66694406638287]
We propose a Conditional Diffusion model based on discrete Graph Structures (CDGS) for molecular graph generation.
Specifically, we construct a forward graph diffusion process on both graph structures and inherent features through differential equations (SDE)
We present a specialized hybrid graph noise prediction model that extracts the global context and the local node-edge dependency from intermediate graph states.
arXiv Detail & Related papers (2023-01-01T15:24:15Z) - Fast Graph Generative Model via Spectral Diffusion [38.31052833073743]
We argue that running full-rank diffusion SDEs on the whole space hinders diffusion models from learning graph topology generation.
We propose an efficient yet effective Graph Spectral Diffusion Model (GSDM), which is driven by low-rank diffusion SDEs on the graph spectrum space.
arXiv Detail & Related papers (2022-11-16T12:56:32Z) - Score-based Generative Modeling of Graphs via the System of Stochastic
Differential Equations [57.15855198512551]
We propose a novel score-based generative model for graphs with a continuous-time framework.
We show that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule.
arXiv Detail & Related papers (2022-02-05T08:21:04Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.