We introduce 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 graphons or GraphSAGE/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.

翻译：我们提出了一种用于图重构的条件流模型——基于先验信息的流匹配（PIFM）。从部分观测数据中重构图结构仍然是一个关键挑战；经典嵌入方法通常缺乏全局一致性，而现代生成模型则难以有效融入结构先验。PIFM通过将基于嵌入的先验知识与连续时间流匹配相结合，弥补了这一差距。基于失真-感知理论的置换等变版本，我们的方法首先利用图子或GraphSAGE/node2vec等先验知识，根据局部信息形成邻接矩阵的知情初始估计。随后应用修正流匹配对该估计进行细化，将其推向干净图的真实分布，并学习全局耦合关系。在不同数据集上的实验表明，PIFM能持续提升经典嵌入方法的性能，在重构精度上超越这些方法及最先进的生成基线模型。