LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening

TL;DR

LGDC introduces a hybrid graph generation framework that combines spectrum-preserving coarsening with diffusion to effectively model both local and global graph properties, improving efficiency and versatility.

Contribution

The paper proposes LGDC, a novel hybrid graph generation method that integrates autoregressive and diffusion approaches through spectrum-preserving coarsening.

Findings

LGDC matches autoregressive models on locally structured datasets.

LGDC performs comparably to diffusion models on globally structured datasets.

The hybrid approach captures both local and global graph properties effectively.

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.