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

TL;DR

LightSBB-M tackles the Schrödinger–Bass Bridge by jointly optimizing drift $α^*$ and volatility $σ^*$ with a tunable parameter $β$, yielding a continuum between diffusion-based and Bass transports. It introduces a dual-based, simulation-free training loop that uses Gaussian-mixture potentials to produce analytic drift and a learned transport map, achieving rapid convergence. Empirical results on synthetic tasks show state-of-the-art $W_2$ transport accuracy, while qualitative and quantitative experiments on unpaired image-to-image translation demonstrate high fidelity and diversity relative to SB and diffusion baselines. The framework scales to high-dimensional data, accommodates heavy-tailed distributions, and provides practical code, broadening the applicability of stochastic-volatility transport in generative modeling and constrained distribution settings.

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.

Figures (12)

• Figure 1: Transport interpolation using SBB: $\mathcal{N}(1,2) \xrightarrow{} \mathcal{N}(0,1)$ (left) and $\delta_0 \xrightarrow{} \mathcal{T}(2)$ (right).
• Figure 2: Evolution of the 2-Wasserstein distance $\mathcal{W}_2$ for different values of $\beta$ on each datasets.
• Figure 3: $\varepsilon=0.1$
• Figure 4: $\varepsilon=1$
• Figure 7: Trajectory from $X_0 \sim p_0$ to $X_1 \sim p_1$ with the underlying $Y$ process.