Prior-Informed Flow Matching for Graph Reconstruction
This work addresses a key challenge in graph reconstruction for applications requiring accurate and consistent graph modeling, representing an incremental improvement by bridging gaps between classical and modern methods.
The paper tackled the problem of reconstructing graphs from partial observations by introducing Prior-Informed Flow Matching (PIFM), which integrates embedding-based priors with continuous-time flow matching to improve global consistency and incorporate structural priors, resulting in enhanced reconstruction accuracy that outperforms classical embeddings and state-of-the-art generative baselines.
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.