Generative Modeling via Nonlinear Schrödinger Bridges and Branching Diffusions

Mathias Grau, Pierre Henry-Labordère · 2026 · arXiv

DOI: 10.48550/arXiv.2610.29476 · open-access PDF

Abstract

We propose a new generative modeling framework grounded in forward-backward partial differential equations (PDEs). These equations arise naturally in mean-field game (MFG) theory, and are closely related to nonlinear Schrödinger systems. Our main contribution is to reinterpret this connection within the setting of generative modeling and to develop an efficient numerical methodology for its practical implementation. Specifically, we derive and characterize a nonlinear extension of the classical Schrödinger bridge problem through a coupled system of PDEs, yielding a model we call SBNL (Schrödin

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