# Transport maps as flows of control-affine systems

arXiv: https://arxiv.org/abs/2404.12793 · HTML: https://mlsanity.com/paper/2404.12793/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Parameter-Efficient Generative Modeling with Controlled Vector Fields](https://mlsanity.com/paper/2605.28267/) (2026)

## Abstract (arXiv)

We consider the problem of transporting notaone probability measure into another through the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the 1-time flow of the system is the optimal transport map for the quadratic cost.