Prior-Informed Flow Matching for Graph Reconstruction

Haoming Chen, Nicolas Zilberstein, Santiago Segarra

Keywords: flow matching, graph inference, inverse problems

TL;DR: We introduce Prior-Informed Flow Matching (PIFM), a conditional flow matching model for graph reconstruction that enhances classical embedding-based predictors by learning a global coupling.

Abstract: 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.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 96