Prior-Informed Flow Matching for Graph Reconstruction

2026-01-29

AI Summary

This work addresses the problem of graph structure reconstruction from partially observed data by proposing a conditional generative framework that integrates embedding priors with continuous flow matching. The method first leverages graph priors—such as graphons or GraphSAGE—to generate an initial adjacency matrix, which is subsequently refined via rectified flow matching to align with the true graph distribution. Its key innovation lies in the first-time incorporation of permutation-equivariant distortion-aware theory into the flow matching paradigm, effectively balancing local structural fidelity with global consistency. Experimental results demonstrate that the proposed approach significantly outperforms existing embedding- and generation-based models across multiple benchmark datasets, achieving notably higher accuracy in graph reconstruction.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• graph reconstruction
• structural priors
• partial observations
• global consistency
• embedding methods

Innovation

• flow matching
• graph reconstruction
• structural priors
• permutation equivariance
• graph generative modeling