LightSBB-M: Bridging Schrödinger and Bass for Generative Diffusion Modeling

The Schrödinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrödinger 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 β > 0 that interpolates between pure drift (the Schrödinger Bridge) and pure volatility (Bass martingale transport). On a Gaussian case with a closed-form solution, we verify that the algorithm recovers the optimal joint plan and both optimal controls, not merely the terminal marginal. We show that LightSBB-M achieves the lowest 2- Wasserstein distance on synthetic datasets against state-of-the-art SB and diffusion baselines with an average of 19% improvement. We also illustrate the generative capability of the framework on an unpaired image-to-image translation task (adult → 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.