EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917100972408832 |
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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 |