LightSBB-M: Bridging Schr\"odinger and Bass for Generative Diffusion Modeling

TL;DR

LightSBB-M is a fast, scalable algorithm for Schr"odinger Bridge problems that improves generative modeling performance on synthetic and real-world tasks, with open-source code available.

Contribution

It introduces LightSBB-M, a novel method that efficiently computes optimal SBB transport plans using a dual representation and a tunable parameter, outperforming existing baselines.

Findings

Achieves up to 32% lower 2-Wasserstein distance on synthetic datasets.

Demonstrates high-fidelity image translation from adult to child faces.

Outperforms state-of-the-art Schr"odinger Bridge and diffusion models.

Abstract

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.