# Flow matching for stochastic linear control systems

arXiv: https://arxiv.org/abs/2412.00617 · HTML: https://mlsanity.com/paper/2412.00617/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2024.

## Built on by (most cited first, 4 of 4)

- [Learning non-equilibrium diffusions with Schr"odinger bridges: from exactly solvable to simulation-free](https://mlsanity.com/paper/2505.16644/) (2025)
- [Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis](https://mlsanity.com/paper/2509.24531/) (2025)
- [Learning Sampled-data Control for Swarms via MeanFlow](https://mlsanity.com/paper/2603.20189/) (2026)
- [Notes on Generative Modeling for Feedback Control and Planning](https://mlsanity.com/paper/2609.33164/) (2026)

## Abstract (arXiv)

This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation comes from applications such as robotic swarms and stochastic thermodynamics, where agents or particles can only be manipulated through control actions. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for special cases, and a numerical procedure is presented to approximate the control law, illustrated with examples.