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

Fuente: arXiv
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Main Authors: Li, Ziyun, Dai, Ben, Hu, Huancheng, Boström, Henrik, Lim, Soon Hoe
Format: Preprint
Published: 2025
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author Li, Ziyun
Dai, Ben
Hu, Huancheng
Boström, Henrik
Lim, Soon Hoe
author_facet Li, Ziyun
Dai, Ben
Hu, Huancheng
Boström, Henrik
Lim, Soon Hoe
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_19087
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching
Li, Ziyun
Dai, Ben
Hu, Huancheng
Boström, Henrik
Lim, Soon Hoe
Machine Learning
Artificial Intelligence
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.
title EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2511.19087