# Federated Flow Matching

arXiv: https://arxiv.org/abs/2509.21250 · HTML: https://mlsanity.com/paper/2509.21250/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Generative Models for Effective ML on Private, Decentralized Datasets](https://mlsanity.com/paper/1911.06679/) (2019)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space](https://mlsanity.com/paper/1910.05954/) (2019)
- [Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling](https://mlsanity.com/paper/2505.13413/) (2025)
- [Training Diffusion Models with Federated Learning](https://mlsanity.com/paper/2406.12575/) (2024)
- [On Fitting Flow Models with Large Sinkhorn Couplings](https://mlsanity.com/paper/2506.05526/) (2025)
- [Federated Learning for Diffusion Models](https://mlsanity.com/paper/2503.06426/) (2025)
- [FedDM: Enhancing Communication Efficiency and Handling Data Heterogeneity in Federated Diffusion Models](https://mlsanity.com/paper/2407.14730/) (2024)

## Abstract (arXiv)

Data today is decentralized, generated and stored across devices and institutions where privacy, ownership, and regulation prevent centralization. This motivates the need to train generative models directly from distributed data locally without central aggregation. In this paper, we introduce Federated Flow Matching (FFM), a framework for training flow matching models under privacy constraints. Specifically, we first examine FFM-vanilla, where each client trains locally with independent source and target couplings, preserving privacy but yielding curved flows that slow inference. We then develop FFM-LOT, which employs local optimal transport couplings to improve straightness within each client but lacks global consistency under heterogeneous data. Finally, we propose FFM-GOT, a federated strategy based on the semi-dual formulation of optimal transport, where a shared global potential function coordinates couplings across clients. Experiments on synthetic and image datasets show that FFM enables privacy-preserving training while enhancing both the flow straightness and sample quality in federated settings, with performance comparable to the centralized baseline.