Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In contrast, energybased models (EBMs) address this by incorporating corresponding scalar energy terms. Here, we propose Energy Matching, a framework that endows flow-based approaches with the flexibility of EBMs. Far from the data manifold, samples move from noise to data along irrotational, optimal transport paths.