Title: Multi-Marginal f-Divergence Schrödinger Bridges: Towards a Unifying Framework for Generation and Distillation
Primary area: generative models
Keywords: Schrodinger Bridges, Optimal Transport, Generative Modeling, Knowledge Distillation.

Abstract: We propose a unified framework for multimodal generation and knowledge distillation by leveraging the Multi-marginal Static Schrödinger Bridge (MSSB) with general f -divergence, where we use flexible and task-oriented prior measures. This approach allows us to adapt the MSSB problem to diverse tasks—from text-guided image generation to model compression—simply by designing an appropriate prior.
For generative modeling, we develop an efficient block-stochastic optimization scheme and a practical Langevin-based inference method. For knowledge distillation, this framework has a clear information-theoretic interpretation: we prove that our MSSB-based Knowledge Distillation (MSSB-KD) implements a variational relaxation of the Information Bottleneck principle. Our novel MSSB-KD formulation demonstrates strong robustness to noisy supervision, significant gains in multi-teacher settings, and scalability across architectures. Finally, we theoretically prove the equivalence between Static and Dynamic Schrödinger Bridges for general
f-divergences, enabling the use of divergences better suited to the task at hand.