EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching

• URL: http://arxiv.org/abs/2511.19087v1
• Date: Mon, 24 Nov 2025 13:27:41 GMT
• Title: EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching
• Authors: Ziyun Li, Ben Dai, Huancheng Hu, Henrik Boström, Soon Hoe Lim,
• Abstract summary: Flow-based generative models synthesize data by integrating a learned velocity field from a reference distribution to the target data distribution.<n>Motivated by classical mechanics, we introduce kinetic path energy (KPE), a simple yet powerful diagnostic that quantifies the total kinetic effort along each generation path of samplers.
• Score: 10.646391583250729
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Flow-based generative models synthesize data by integrating a learned velocity field from a reference distribution to the target data distribution. Prior work has focused on endpoint metrics (e.g., fidelity, likelihood, perceptual quality) while overlooking a deeper question: what do the sampling trajectories reveal? Motivated by classical mechanics, we introduce kinetic path energy (KPE), a simple yet powerful diagnostic that quantifies the total kinetic effort along each generation path of ODE-based samplers. Through comprehensive experiments on CIFAR-10 and ImageNet-256, we uncover two key phenomena: ({i}) higher KPE predicts stronger semantic quality, indicating that semantically richer samples require greater kinetic effort, and ({ii}) higher KPE inversely correlates with data density, with informative samples residing in sparse, low-density regions. Together, these findings reveal that semantically informative samples naturally reside on the sparse frontier of the data distribution, demanding greater generative effort. Our results suggest that trajectory-level analysis offers a physics-inspired and interpretable framework for understanding generation difficulty and sample characteristics.

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