Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge

Titouan Vayer

Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge

机器学习 2026-06-29 v1 机器学习

作者: Titouan Vayer

摘要

These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr{\"o}dinger bridge and flow matching.

引用

@article{arxiv.2606.30053,
  title  = {Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge},
  author = {Titouan Vayer},
  journal= {arXiv preprint arXiv:2606.30053},
  year   = {2026}
}