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, energy-based 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.