DiPhon：基于图子上的扩散用于可扩展图生成
DiPhon: Diffusion on Graphons for Scalable Graph Generation
AI总结：
研究如何将扩散模型扩展到大型图，通过图子提出DiPhon框架，制定连续扩散过程并推导逆时间过程，证明其与连续图子过程的矩匹配，实验展示了在小图训练后生成大图的可扩展性。
摘要：
扩散模型是图生成的主要范式，在分子设计等领域有显著影响。但将这些模型扩展到大型图仍是未解决问题。我们通过图子（密集图序列与大小无关的极限对象）来研究密集图设置下结构统计如何随节点大小尺度变化，从而提出DiPhon，一种用于大小可扩展图生成的扩散框架。具体而言，通过雅可比随机微分方程在图子空间制定连续扩散过程，并提出离散图级过程来模仿有限图上的这些动态。我们还推导了相应的逆时间过程，其得分有易处理形式，通过图去噪从数据估计并用于生成图样本。证明DiPhon与连续图子过程诱导的边际分布的一阶矩完全匹配，二阶矩近似到一个封闭形式的差异。通过在小图上训练并在推理时生成更大图展示了其可扩展性，且保留核心拓扑属性。
英文摘要：
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.
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