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

TMLR Paper5358 Authors

Abstract: Flow matching has emerged as a powerful generative modeling approach with flexible source distribution choices. 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 under the 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 paradoxically degrades 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 robust omnidirectional supervision essential for stable flow learning, while eliminating data sparse-region initializations 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 insight and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models.

Submission Length: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Anuroop_Sriram1

Submission Number: 5358