Variational Flow Matching for Graph Generation

TL;DR

This paper introduces variational flow matching (VFM), a new framework for graph generation that unifies flow matching and score-based models, demonstrating strong empirical results with the proposed CatFlow method.

Contribution

The paper develops VFM as a novel variational inference formulation of flow matching, and introduces CatFlow, a new efficient method for categorical graph generation.

Findings

CatFlow outperforms existing models on graph and molecular generation tasks.

VFM unifies flow matching and score-based models with theoretical insights.

CatFlow is easy to implement and computationally efficient.

Abstract

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.