轻量级算法快速求解生成扩散模型中的最优传输路径。
LightSBB-M: Bridging Schrödinger and Bass for Generative Diffusion Modeling
- 基于对偶形式解析求解最优漂移与波动，仅需少数迭代。
- 在合成数据上2-Wasserstein距离降低最多32%，优于现有方法。
- 可调参数实现漂移与波动的灵活切换，适合图像生成任务。
Schrödinger桥与Bass（SBB）框架联合控制漂移与波动，是经典Schrödinger桥的扩展。本文提出LightSBB-M，一种仅需少数迭代即可计算最优SBB传输方案的算法。该方法利用SBB目标函数的对偶表示，获得最优漂移与波动的解析表达式，并引入大于零的可调参数beta，实现纯漂移（Schrödinger桥）与纯波动（Bass鞅传输）之间的插值。实验表明，LightSBB-M在合成数据集上的2-Wasserstein距离达到最低，相比先进SB与扩散基线最高提升32%。同时，该框架在无配对图像到图像翻译任务（如FFHQ中成人转儿童面部）中展现出良好生成能力。结果证明，LightSBB-M是一种高效、高保真且可扩展的SBB求解器，在合成与真实世界生成任务中均超越现有基准。代码已开源。
原文摘要 · Abstract (English)
The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that computes the optimal SBB transport plan in only a few iterations. The method exploits a dual representation of the SBB objective to obtain analytic expressions for the optimal drift and volatility, and it incorporates a tunable parameter beta greater than zero that interpolates between pure drift (the Schrodinger Bridge) and pure volatility (Bass martingale transport). We show that LightSBB-M achieves the lowest 2-Wasserstein distance on synthetic datasets against state-of-the-art SB and diffusion baselines with up to 32 percent improvement. We also illustrate the generative capability of the framework on an unpaired image-to-image translation task (adult to child faces in FFHQ). These findings demonstrate that LightSBB-M provides a scalable, high-fidelity SBB solver that outperforms existing SB and diffusion baselines across both synthetic and real-world generative tasks. The code is available at https://github.com/alexouadi/LightSBB-M.
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