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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{ö}dinger bridge and flow matching.
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Foundations of Schrödinger Bridges for Generative Modeling
The Fundamental Limits of Valid Transport Map Estimation
Exploring Diffusion and Flow Matching Under Generator Matching
On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields
ROMS-IMLE: A Minimalist Approach to Competitive Single-Step Generative Modelling
Branched Optimal Transport Amortization
@article{vayer2026notes,
title = {Notes on generative modeling: flow matching, diffusion, optimal transport and Schr{ö}dinger bridge},
author = {Titouan Vayer},
year = {2026},
eprint = {2606.30053},
archivePrefix = {arXiv},
url = {http://arxiv.org/abs/2606.30053v1}
}Shows whether official code is linked for this paper.
[](https://codeofpaper.com/paper/2606.30053)