# Notes on Generative Modeling for Feedback Control and Planning

arXiv: https://arxiv.org/abs/2609.33164 · HTML: https://mlsanity.com/paper/2609.33164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 8 of its 51 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 8 of 8)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Benamou-Brenier Formulation of Optimal Transport for Nonlinear Control Systems on Rd](https://mlsanity.com/paper/2407.16088/) (2024)
- [Flow matching for stochastic linear control systems](https://mlsanity.com/paper/2412.00617/) (2024)
- [Flow Matching for Measure Transport and Feedback Stabilization of Control-Affine Systems](https://mlsanity.com/paper/2510.02706/) (2025)
- [Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems](https://mlsanity.com/paper/2504.09836/) (2025)
- [Optimal transport over nonlinear systems via infinitesimal generators on graphs](https://mlsanity.com/paper/1612.01193/) (2016)

## Abstract (arXiv)

In these notes, we view control as a dynamically constrained sampling problem on the state-space of a control system. With this viewpoint, we extend methods from generative modeling, such as flow matching, normalizing flows and denoising diffusions to control problems. Concepts such as controllability, optimal control and trajectory planning play an important role in guiding the extension and understanding well-posedeness of the corresponding algorithms, with application to steering systems to target states or distributions and sampling from reachable sets. The notes are intended as an accessible introduction for readers with a background in control theory and robotics.