Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis

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 Restoration, 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 \url{https://github.com/zhukaizhen/diffusion_bridge_flow_matching}.

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. This paper provides a unified comparison of the two methods. We recast them through the lens of Stochastic Optimal Control and prove that Diffusion Bridge tends to guide transformations through more stable and natural trajectories, making it more reliable when tasks are difficult or training data is limited. From the perspective of Optimal Transport, Flow Matching is simpler but can become less robust when the training data size is reduced. Using the same model design for a fair comparison, we test both methods on image restoration, translation, style transfer tasks and so on. The results show that Diffusion Bridge is generally stronger in difficult cases, while Flow Matching remains useful when simplicity and speed are most important.