用物理能量分析生成路径，揭示高质量图像来自高能耗稀疏区域。
EnfoPath: Energy-Informed Analysis of Generative Trajectories in Flow Matching
- 引入动能路径能量KPE，量化生成过程中的总能量消耗
- 高KPE样本语义更丰富，且多位于数据低密度区
- 适合关注生成机制解释与采样质量评估的研究者
基于流的生成模型通过积分学习到的速度场，将参考分布逐步变换至目标数据分布。以往工作多关注终点指标（如保真度、似然、感知质量），忽视了采样轨迹本身蕴含的信息。受经典力学启发，我们提出动能路径能量（KPE），一种简单而有效的诊断工具，用于量化基于ODE的采样器在每条生成路径上的总动能消耗。在CIFAR-10和ImageNet-256上的大量实验揭示两个关键现象：(i) 较高的KPE能预测更强的语义质量，表明语义丰富的样本需要更大的动能投入；(ii) 高KPE与数据密度呈负相关，信息量大的样本集中在稀疏的低密度区域。这些发现表明，语义信息丰富的样本自然位于数据分布的稀疏边界上，生成过程需更高能量。结果表明，轨迹级分析提供了一种受物理启发且可解释的框架，用于理解生成难度与样本特性。
原文摘要 · Abstract (English)
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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