用结构先验指导图重建，提升生成图的全局一致性。
Prior-Informed Flow Matching for Graph Reconstruction
- 结合嵌入模型先验与连续时间流匹配，生成更合理的图结构。
- 在多个数据集上优于经典嵌入方法和前沿生成模型。
- 适合需要高质量图重建的应用，如社交网络分析。
我们提出一种用于图重建的条件流模型——先验引导流匹配（PIFM）。从部分观测中重构图仍是关键挑战：传统嵌入方法常缺乏全局一致性，而现代生成模型难以融入结构先验。PIFM通过将基于嵌入的先验与连续时间流匹配相结合，弥补这一差距。基于排列等变的失真-感知理论，该方法首先利用如GraphSAGE或node2vec等先验，基于局部信息形成邻接矩阵的初始估计；随后采用修正流匹配对齐该估计至干净图的真实分布，并学习全局耦合关系。在多个数据集上的实验表明，PIFM持续提升经典嵌入方法表现，在重建精度上超越它们及当前最优生成基线。
原文摘要 · Abstract (English)
We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while modern generative models struggle to incorporate structural priors. PIFM bridges this gap by integrating embedding-based priors with continuous-time flow matching. Grounded in a permutation equivariant version of the distortion-perception theory, our method first uses a prior, such as GraphSAGE or node2vec, to form an informed initial estimate of the adjacency matrix based on local information. It then applies rectified flow matching to refine this estimate, transporting it toward the true distribution of clean graphs and learning a global coupling. Experiments on different datasets demonstrate that PIFM consistently enhances classical embeddings, outperforming them and state-of-the-art generative baselines in reconstruction accuracy.
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