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.

翻译：针对离散域（如图形）的能量模型能够显式捕获相对似然，天然支持条件生成或测试时约束执行等可组合概率推理任务。然而，离散能量模型通常难以实现高效高质量的采样，因为支撑区域外的虚假局部最小值会困住采样器并导致训练不稳定。这种缺陷历史上导致其与离散扩散模型之间存在保真度差距。我们提出Graph Energy Matching（GEM），一种弥合该保真度差距的图生成框架。受Jordan-Kinderlehrer-Otto（JKO）方案中传输图优化视角的启发，GEM学习一个置换不变势能，该势能同时提供从噪声到数据的传输对齐引导，并在高数据似然区域内优化样本。此外，我们引入一种采样协议，通过基于能量的切换无缝衔接：（i）向高概率区域的快速梯度引导传输与（ii）用于探索学习图分布的混合机制。在分子图基准测试中，GEM达到或超越强离散扩散基线。除样本质量外，相对似然的显式建模支持推理时的定向探索，便于组合生成、属性约束采样以及图之间的测地线插值。