混合生成图结构，兼顾局部细节与全局模式。
LGDC: Latent Graph Diffusion via Spectrum-Preserving Coarsening
- 通过谱保持的粗化-细化映射，建立图与潜在空间双向通道。
- 在树状、平面和社区数据集上性能媲美专用模型。
- 适合需要同时关注局部和全局结构的图生成任务。
图生成是科学领域中的关键任务。现有方法主要分为两类：自回归模型（逐次扩展图）和单步模型（如扩散模型，一次性生成完整图）。本文分析发现二者存在核心权衡：自回归模型更擅长捕捉局部结构（如度分布、聚类系数），而单步模型在建模全局模式（如谱分布）上表现更优。为此，提出LGDC（基于谱保持粗化的潜在图扩散）框架，通过谱保持的粗化-细化过程，在图与潜在空间间双向映射，利用扩散高效生成潜在图后，再通过展开恢复细节。该设计同时捕捉局部与全局特性，提升效率。实验表明，LGDC在局部结构数据集（Tree）上性能媲美自回归模型，在全局结构数据集（Planar, Community-20）上达到扩散模型水平，验证了混合生成的优势。
原文摘要 · Abstract (English)
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.
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