# Learning Sampled-data Control for Swarms via MeanFlow

arXiv: https://arxiv.org/abs/2603.20189 · HTML: https://mlsanity.com/paper/2603.20189/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025)
- [Density control of interacting agent systems](https://mlsanity.com/paper/2108.07342/) (2021)
- [OAT-FM: Optimal Acceleration Transport for Improved Flow Matching](https://mlsanity.com/paper/2509.24936/) (2025)
- [Flow matching for stochastic linear control systems](https://mlsanity.com/paper/2412.00617/) (2024)
- [Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems](https://mlsanity.com/paper/2504.09836/) (2025)
- [Mean field type control with species dependent dynamics via structured tensor optimization](https://mlsanity.com/paper/2305.15292/) (2023)
- [Efficient Iterative Proximal Variational Inference Motion Planning](https://mlsanity.com/paper/2411.03416/) (2024)

## Abstract (arXiv)

Steering large-scale swarms with only limited control updates is often needed due to communication or computational constraints, yet most learning-based approaches do not account for this and instead model instantaneous velocity fields. As a result, the natural object for decision making is a finite-window control quantity rather than an infinitesimal one. To address this gap, we consider the recent machine learning framework MeanFlow and generalize it to the setting with general linear dynamic systems. This results in a new sampled-data learning framework that operates directly in control space and that can be applied for swarm steering. To this end, we learn the finite-horizon coefficient that parameterizes the minimum-energy control applied over each interval, and derive a differential identity that connects this quantity to a local bridge-induced supervision signal. This identity leads to a simple stop-gradient regression objective, allowing the interval coefficient field to be learned efficiently from bridge samples. The learned policy is deployed through sampled-data updates, guaranteeing that the resulting controller exactly respects the prescribed linear time-invariant dynamics and actuation channel. The resulting method enables few-step swarm steering at scale, while remaining consistent with the finite-window actuation structure of the underlying control system.