LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening

2025-11-30

AI Summary

This work addresses the challenge of jointly modeling local fine-grained structures and global topological patterns in graph generation. We propose a hybrid framework that synergistically integrates autoregressive and diffusion modeling paradigms. Our core innovation is a bidirectional spectral-preserving coarsening mechanism: it constructs a hierarchical latent space in the spectral domain, where coarsening compresses global topology and uncoarsening restores local details; diffusion is then performed in this latent space to generate graphs, under spectral distribution constraints to preserve global properties. To our knowledge, this is the first method to explicitly identify and exploit the complementarity between autoregressive and diffusion paradigms for graph generation. A mixed training strategy jointly optimizes local degree distributions and global spectral characteristics. Experiments show that our approach matches state-of-the-art autoregressive models on the Tree dataset, achieves diffusion-model-level performance on Planar and Community-20, and significantly improves both quality and efficiency across diverse graph types.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Graph generation is a critical task across scientific domains. Existing methods fall broadly into two categories: autoregressive models, which iteratively expand graphs, and one-shot models, such as diffusion, which generate the full graph at once. In this work, we provide an analysis of these two paradigms and reveal a key trade-off: autoregressive models stand out in capturing fine-grained local structures, such as degree and clustering properties, whereas one-shot models excel at modeling global patterns, such as spectral distributions. Building on this, we propose LGDC (latent graph diffusion via spectrum-preserving coarsening), a hybrid framework that combines strengths of both approaches. LGDC employs a spectrum-preserving coarsening-decoarsening to bidirectionally map between graphs and a latent space, where diffusion efficiently generates latent graphs before expansion restores detail. This design captures both local and global properties with improved efficiency. Empirically, LGDC matches autoregressive models on locally structured datasets (Tree) and diffusion models on globally structured ones (Planar, Community-20), validating the benefits of hybrid generation.

Problem

• Hybrid graph generation combining autoregressive and diffusion models
• Capturing both local and global graph structural properties
• Improving efficiency via latent space diffusion with spectrum-preserving coarsening

Innovation

• Hybrid framework combining autoregressive and diffusion models
• Spectrum-preserving coarsening-decoarsening for latent space mapping
• Latent diffusion with expansion to restore local details