用高阶拓扑引导扩散模型生成更真实的图结构。
HOG-Diff: Higher-Order Guided Diffusion for Graph Generation
- 通过高阶拓扑信息指导图的分步生成过程
- 在8个基准上均优于现有方法，尤其在高阶拓扑指标上提升显著
- 适合需要精确拓扑结构的图生成任务
图生成是一项关键但具有挑战性的任务，需深入理解复杂的非欧几里得结构。尽管扩散模型在图生成中取得进展，但多数方法沿用图像生成框架，忽视了图的高阶拓扑特性，限制了对图结构的捕捉能力。本文提出一种基于高阶拓扑引导的扩散模型（HOG-Diff），采用从粗到细的生成流程，通过扩散桥实现，能逐步生成具备内在拓扑结构的合理图。我们证明该模型在理论上强于经典扩散框架。在涵盖多个领域且包含大规模设置的8个图生成基准上进行的广泛实验表明，该方法具备良好可扩展性，并在成对及高阶拓扑指标上表现优异。
原文摘要 · Abstract (English)
Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are typically adapted from image generation frameworks and overlook inherent higher-order topology, limiting their ability to capture graph topology. In this work, we propose Higher-order Guided Diffusion (HOG-Diff), a principled framework that progressively generates plausible graphs with inherent topological structures. HOG-Diff follows a coarse-to-fine generation curriculum, guided by higher-order topology and implemented via diffusion bridges. We further prove that our model admits stronger theoretical guarantees than classical diffusion frameworks. Extensive experiments across eight graph generation benchmarks, spanning diverse domains and including large-scale settings, demonstrate the scalability of our method and its superior performance on both pairwise and higher-order topological metrics. Our project page is available \href{https://circle-group.github.io/research/hog-diff/}{here}.
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