# OAT-FM: Optimal Acceleration Transport for Improved Flow Matching

arXiv: https://arxiv.org/abs/2509.24936 · HTML: https://mlsanity.com/paper/2509.24936/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 44 of its 56 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 44)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (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)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)

## Built on by (most cited first, 7 of 7)

- [WAM-Flow: Parallel Coarse-to-Fine Motion Planning via Discrete Flow Matching for Autonomous Driving](https://mlsanity.com/paper/2512.06112/) (2025)
- [Isokinetic Flow Matching for Pathwise Straightening of Generative Flows](https://mlsanity.com/paper/2604.04491/) (2026)
- [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026)
- [Bridging Vision and Language Concepts through Optimal Transport Semantic Flow](https://mlsanity.com/paper/2606.26891/) (2026)
- [Learning Sampled-data Control for Swarms via MeanFlow](https://mlsanity.com/paper/2603.20189/) (2026)
- [Improving Function Space Flow Matching with Kernel Optimal Transport](https://mlsanity.com/paper/2609.38049/) (2026)
- [VTV-FM: Flow Matching through Variational Terminal-Velocity Closure](https://mlsanity.com/paper/2610.00785/) (2026)

## Abstract (arXiv)

As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this study, we bridge FM and the recent theory of Optimal Acceleration Transport (OAT), developing an improved FM method called OAT-FM and exploring its benefits in both theory and practice. In particular, we demonstrate that the straightening objective hidden in existing OT-based FM methods is mathematically equivalent to minimizing the physical action associated with acceleration defined by OAT. Accordingly, instead of enforcing constant velocity, OAT-FM optimizes the acceleration transport in the product space of sample and velocity, whose objective corresponds to a necessary and sufficient condition of flow straightness. An efficient algorithm is designed to achieve OAT-FM with low complexity. OAT-FM motivates a new two-phase FM paradigm: Given a generative model trained by an arbitrary FM method, whose velocity information has been relatively reliable, we can fine-tune and improve it via OAT-FM. This paradigm eliminates the risk of data distribution drift and the need to generate a large number of noise data pairs, which consistently improves model performance in various generative tasks. Code is available at: https://github.com/AngxiaoYue/OAT-FM