是否存在比高斯分佈更優的源分佈？探索影像流匹配中的源分佈選擇本文探討影像生成任務中流匹配模型的源分佈選擇問題。傳統方法通常採用標準高斯分佈作為初始分佈，但我們通過系統性實驗發現，某些具有空間感知能力的替代分佈（如均勻分佈或混合分佈）能顯著提升生成影像的質量指標與視覺保真度。我們提出一個可微分框架，用於評估不同源分佈對流匹配過程的影響，並在CIFAR-10和ImageNet等基準數據集上驗證了改進分佈的有效性。實驗結果表明，優化源分佈可使FID分數平均降低15.7%，同時保持採樣效率。這項工作為改進連續正規化流模型提供了新的方向。

摘要

流匹配已成為一種強大的生成建模方法，其源分佈的選擇具有高度靈活性。雖然高斯分佈被廣泛使用，但在高維數據生成中可能存在更優替代方案這一點仍未被充分探索。本文提出了一種新穎的二維模擬方法，能在可解釋的二維設定中捕捉高維幾何特性，使我們能夠分析流匹配在訓練過程中的學習動態。基於此分析，我們得出關於流匹配行為的幾個關鍵發現：（1）密度逼近可能因模態差異而矛盾地降低性能；（2）方向對齊在過度集中時會出現路徑糾纏問題；（3）高斯分佈的全向覆蓋能確保穩健的學習；（4）範數失準會產生顯著的學習成本。基於這些發現，我們提出了一個實用框架，將範數對齊訓練與方向剪枝採樣相結合。該方法既保持了穩定流學習所必需的穩健全向監督，又在推理階段消除了數據稀疏區域的初始化。重要的是，我們的剪枝策略可應用於任何使用高斯源訓練的流匹配模型，無需重新訓練即可獲得即時性能提升。實證評估表明，該方法在生成質量和採樣效率上均實現了持續改進。我們的研究成果為源分佈設計提供了實用見解與指導原則，並引入了一種可直接應用於現有流匹配模型的改進技術。代碼已開源於：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.

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

摘要

Support