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

2025-09-29

AI Summary

While both Diffusion Bridges and Flow Matching achieve strong performance in arbitrary distribution transformation, their theoretical trade-offs remain unclear due to divergent modeling assumptions and implementation differences, hindering unified analysis. Method: We establish the first unified analytical framework grounded in stochastic optimal control and optimal transport theory. From a control-theoretic perspective, we formally prove that Diffusion Bridges minimize a strictly superior cost functional and identify Flow Matching’s intrinsic failure in low-sample interpolation as a fundamental limitation. We further propose a latent Transformer-based unified architecture enabling fair empirical comparison. Results: Experiments across image inpainting, super-resolution, and other tasks validate our theoretical predictions: Diffusion Bridges significantly outperform Flow Matching under data scarcity or large source–target distribution divergence.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 https://anonymous.4open.science/r/DBFM-3E8E/.

Problem

• Comparing Diffusion Bridge and Flow Matching for distribution transformation tasks
• Analyzing theoretical performance differences through unified framework
• Evaluating models across various image processing tasks systematically

Innovation

• Unified Stochastic Optimal Control framework for Diffusion Bridge and Flow Matching
• Latent Transformer architecture for Diffusion Bridge implementation
• Systematic comparison across six image processing tasks