Fast Graph Generation via Spectral Diffusion.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Graph Theory

Background:

• Generating graph-structured data is complex, requiring accurate distribution learning.
• Diffusion models show state-of-the-art performance but face limitations in graph topology generation.
• Full-rank diffusion on adjacency matrices hinders quality in generated graph data.

Purpose of the Study:

• To propose an efficient and effective Graph Spectral Diffusion Model (GSDM).
• To address limitations in current diffusion models for graph generation.
• To improve the quality and efficiency of generated graph data.

Main Methods:

• Developed a Graph Spectral Diffusion Model (GSDM).
• Utilized low-rank diffusion stochastic differential equations (SDEs) on the graph spectrum space.
• Provided theoretical guarantees for the spectral diffusion model.

Main Results:

• GSDM demonstrated superior graph generation quality compared to baseline models.
• The proposed model achieved significantly lower computational consumption.
• Experiments confirmed GSDM as a state-of-the-art (SOTA) model across various datasets.

Conclusions:

• Graph Spectral Diffusion Model (GSDM) effectively addresses limitations of standard diffusion models.
• Low-rank diffusion on the graph spectrum enhances topology learning and data quality.
• GSDM offers a more efficient and higher-quality solution for graph generation.