New paper: generative modeling via nonlinear Schrödinger bridges and branching diffusions, validated on MNIST/FFHQ
chaumian · x · 2026-10-23
An arXiv paper by Mathias Grau and Pierre Henry-Labordère proposes a generative modeling framework grounded in forward-backward PDEs from mean-field game theory, closely related to nonlinear Schrödinger systems.
- Reinterprets this connection for generative modeling and derives SBNL, a nonlinear extension of the classical Schrödinger bridge problem characterized by coupled PDEs.
- The solver uses branching diffusions and probabilistic representations of semilinear PDEs — embarrassingly parallel, scalable to high dimensions, and applicable to broad nonlinear interaction functionals.
- Validated via recovery of the classical Schrödinger bridge, nonlinear extensions (Gross-Pitaevskii penalties, potential interactions), and high-dimensional generation on MNIST and FFHQ.
- The same framework embeds score-based generative modeling, diffusion models, and tractable Gaussian Schrödinger bridges.
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