是否存在优于高斯分布的源分布？探索图像流匹配中的源分布选择

Is There a Better Source Distribution than Gaussian? Exploring Source Distributions for Image Flow Matching

December 20, 2025

作者: Junho Lee, Kwanseok Kim, Joonseok Lee

cs.AI

摘要

流匹配作为一种生成建模方法，凭借其灵活的源分布选择而展现出强大潜力。虽然高斯分布被广泛采用，但在高维数据生成中可能存在更优替代方案这一点仍未被充分探索。本文提出了一种新颖的二维仿真方法，通过在可解释的二维环境中捕捉高维几何特性，使我们能够分析流匹配在训练过程中的学习动态。基于此分析，我们得出关于流匹配行为的若干关键发现：（1）密度逼近可能因模式差异而适得其反；（2）方向对齐在过度集中时会出现路径纠缠；（3）高斯分布的全向覆盖能确保稳健学习；（4）范数失准会导致显著的学习成本。基于这些发现，我们提出了一种结合范数对齐训练与方向剪枝采样的实用框架。该方法既保持了稳定流学习所必需的全向监督机制，又在推理阶段避免了数据稀疏区域的初始化。重要的是，我们的剪枝策略可应用于任何采用高斯源训练的流匹配模型，无需重新训练即可实现即时性能提升。实证评估表明，该方法在生成质量和采样效率上均能实现持续改进。我们的研究为源分布设计提供了实用见解与指导原则，并引入了一种可直接应用于改进现有流匹配模型的技术。代码已开源：https://github.com/kwanseokk/SourceFM。

English

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.