Abstract
Diffusion Bridge and Flow Matching have both demonstrated compelling empirical performance in transformation between arbitrary distributions. However, there remains confusion about which approach is generally preferable, and the substantial discrepancies in their modeling assumptions and practical implementations have hindered a unified theoretical account of their relative merits. We have, for the first time, provided a unified theoretical and experimental validation of these two models. We recast their frameworks through the lens of Stochastic Optimal Control and prove that the cost function of the Diffusion Bridge is lower, guiding the system toward more stable and natural trajectories. Simultaneously, from the perspective of Optimal Transport, interpolation coefficients $t$ and $1-t$ of Flow Matching become increasingly ineffective when the training data size is reduced. To corroborate these theoretical claims, we propose a novel, powerful architecture for Diffusion Bridge built on a latent Transformer, and implement a Flow Matching model with the same structure to enable a fair performance comparison in various experiments. Comprehensive experiments are conducted across Image Inpainting, Super-Resolution, Deblurring, Denoising, Translation, and Style Transfer tasks, systematically varying both the distributional discrepancy (different difficulty) and the training data size. Extensive empirical results align perfectly with our theoretical predictions and allow us to delineate the respective advantages and disadvantages of these two models. Our code is available at this https URL.
Abstract (translated)
扩散桥（Diffusion Bridge）和流匹配（Flow Matching）在任意分布之间的转换中都展示了令人信服的实证性能。然而，关于哪一种方法更优的选择仍然存在疑惑，并且这两种模型之间巨大的建模假设差异及实际实现上的不同也阻碍了对它们相对优势进行统一理论阐述的可能性。我们首次提供了这两种模型统合理论和实验验证的方法。我们将这两个框架重新构想为随机最优控制的视角，并证明扩散桥的成本函数较低，这有助于系统趋向更稳定且自然的轨迹变化。同时，从最优传输的角度来看，在训练数据量减少的情况下，流匹配中的插值系数 $t$ 和 $1-t$ 逐渐变得无效。 为了验证这些理论主张，我们提出了一种新颖而强大的基于潜在Transformer架构的扩散桥模型，并实现了一个结构相同的流匹配模型以在各种实验中进行公平性能比较。我们在图像修复、超分辨率、去模糊化、去噪、转换以及风格迁移等任务上进行了全面实验，系统地改变分布差异（不同难度）和训练数据量。广泛的实证结果与我们的理论预测完全一致，并使我们能够明确指出这两种模型各自的优缺点。 有关该工作的代码可以在提供的链接中获取。
URL
https://arxiv.org/abs/2509.24531
