arXiv:2607.07232stat.MLcs.AI2026-07

用图论极限思想实现大图生成,无需重训即可扩展图规模。

DiPhon: Diffusion on Graphons for Scalable Graph Generation

论文配图:DiPhon: Diffusion on Graphons for Scalable Graph Generation
图 1 · 摘自论文原文
  • 在图极限空间上构建连续扩散过程,通过雅可比SDE建模图结构演化
  • 生成的图在节点数增长时仍保持核心拓扑特征,首尾阶矩匹配良好
  • 适合需要生成超大规模图且不希望重新训练的科研与工业场景

扩散模型是图生成的主流方法,在分子设计等领域有重要影响。然而,将其扩展到大规模图仍是未解难题。本文从稠密图序列的极限对象——图论(graphon)出发,研究图结构统计量在不同节点规模下的行为。基于此提出DiPhon:一种在图论空间上通过雅可比随机微分方程构建的连续扩散过程,并设计离散化图级生成流程以模拟其动态。我们推导了反向过程所需边际得分,发现其具有可解析形式,可通过图去噪从数据中估计并用于采样。理论证明,DiPhon精确匹配连续图论过程的首阶矩,二阶矩近似误差具闭式表达。因此,该方法继承了图论动态的关键尺度无关统计特性,为可扩展图生成提供了理论保障。实验表明,仅在小图上训练后,可在推理阶段生成越来越大的图,无需重训,同时保留核心拓扑性质。

原文摘要 · Abstract (English)

Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem. We approach this question in the dense-graph setting through the lens of graphons, the size-agnostic limit objects of dense graph sequences, to study how structural graph statistics behave across node-size scales. This perspective leads to DiPhon, a diffusion framework for size-scalable graph generation. Specifically, we formulate a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), and propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs. We further derive the corresponding reverse-time process, which requires access to the marginal score. For the Jacobi process, this score interestingly admits a tractable form, which we estimate from data via graph denoising and plug into the reverse process to generate graph samples. We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy. Thus, DiPhon inherits key size-agnostic statistical properties of the graphon dynamics, providing a principled route toward scalable graph generation. Empirically, we demonstrate this scalability by training on small graphs and generating progressively larger graphs at inference time, without retraining, while preserving their core topological properties.

图生成扩散模型图论可扩展性

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