🤖 AI Summary
This work addresses the computational bottleneck in jointly controlling drift and diffusion in generative diffusion models by proposing the LightSBB-M algorithm. Within the Schrödinger Bridge and Bass (SBB) joint modeling framework, it achieves the first analytical solution to the SBB problem. By leveraging a dual representation of the objective function, the method explicitly derives the optimal drift and diffusion coefficients and introduces a tunable parameter β to continuously interpolate between them, thereby unifying the Schrödinger bridge and Bass transport mechanisms. The approach significantly enhances both computational efficiency and generation quality: on synthetic data, it reduces the 2-Wasserstein distance by up to 32% compared to existing methods, and demonstrates high-fidelity unpaired image translation in the challenging task of adult-to-child face conversion on FFHQ.
📝 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.