Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation

2026-03-24

AI Summary

This work proposes a novel energy-based framework for graph generation that overcomes the limitations of conventional discrete energy models—namely, poor sampling efficiency and susceptibility to spurious local minima—by introducing, for the first time in graph generation, the JKO (Jordan–Kinderlehrer–Otto) scheme’s transport map perspective. The method learns a permutation-invariant potential function to align the transport from noise to data distributions and incorporates an adaptive energy-switching mechanism that dynamically balances between rapid guidance and refined mixing. This approach naturally supports compositional generation, attribute-constrained sampling, and geodesic interpolation between graphs. On molecular graph benchmarks, it achieves generation quality on par with or superior to state-of-the-art discrete diffusion models while significantly enhancing inference flexibility and the ability to explore the target distribution.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs 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
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities. This has historically resulted in a fidelity gap relative to discrete diffusion models. We introduce Graph Energy Matching (GEM), a generative framework for graphs that closes this fidelity gap. Motivated by the transport map optimization perspective of the Jordan-Kinderlehrer-Otto (JKO) scheme, GEM learns a permutation-invariant potential energy that simultaneously provides transport-aligned guidance from noise toward data and refines samples within regions of high data likelihood. Further, we introduce a sampling protocol that leverages an energy-based switch to seamlessly bridge: (i) rapid, gradient-guided transport toward high-probability regions to (ii) a mixing regime for exploration of the learned graph distribution. On molecular graph benchmarks, GEM matches or exceeds strong discrete diffusion baselines. Beyond sample quality, explicit modeling of relative likelihood enables targeted exploration at inference time, facilitating compositional generation, property-constrained sampling, and geodesic interpolation between graphs.

Problem

• energy-based models
• graph generation
• sampling efficiency
• fidelity gap
• discrete domains

Innovation

• Energy-based modeling
• Graph generation
• Transport alignment
• JKO scheme
• Permutation-invariant potential