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

Abstract:

The generative modeling of discrete structures like graphs is a critical component in numerous scientific and industrial fields, ranging from materials design to molecular discovery. In these areas, probabilistic inference offers significant advantages, allowing for the composition of generated samples and the rigorous integration of specific constraints, such as functional or structural attributes. Energy-based models are well-suited for this purpose because they capture relative likelihoods and permit the direct enforcement of constraints during the inference process, thereby facilitating composable generation.

However, discrete energy-based models often face challenges regarding sampling efficiency and quality. Regions outside the data support frequently harbor spurious local minima, which can trap sampling algorithms and lead to training instability. Consequently, these models often exhibit a fidelity gap when compared to discrete diffusion models. To bridge this divide, we present Graph Energy Matching (GEM), a discrete generative framework grounded in the Jordan-Kinderlehrer-Otto (JKO) transport-map optimization perspective. GEM learns a potential energy function that is invariant to permutations, simultaneously directing discrete transport from noise toward high-likelihood graph areas and refining samples within those regions.

We also propose a novel sampling protocol that employs an energy-based switching strategy. This approach effectively combines rapid, gradient-guided transport with a local mixing regime to ensure robust exploration. Evaluations on molecular graph benchmarks demonstrate that GEM performs on par with or exceeds strong discrete diffusion baselines across most standard metrics. Furthermore, beyond enhancing generation quality, GEM’s capacity to model relative likelihoods supports targeted exploration, enabling compositional generation, sampling constrained by properties, and interpolation between different graphs.

Project page: https://michalbalcerak.ai/graph-energy-matching/

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC