Prior-Informed Flow Matching for Graph Reconstruction

TL;DR

This paper presents Prior-Informed Flow Matching (PIFM), a novel graph reconstruction method that combines structural priors with flow matching to improve accuracy over existing models.

Contribution

PIFM introduces a new approach integrating embedding priors with continuous flow matching for more accurate graph reconstruction.

Findings

PIFM outperforms classical embedding methods in accuracy.

PIFM surpasses state-of-the-art generative models.

The method effectively incorporates structural priors.

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.