Optimal Transport Flow Matching by Design
This paper proposes a new approach to optimal transport flow matching by treating the prior as a design choice rather than a fixed input, avoiding the intractable computation of OT coupling in high dimensions. The authors identify low-frequency projection of natural images as a prior that admits an OT-optimal identity coupling with data, reducing the flow matching task to synthesizing high-frequency details. The method requires no modifications to the flow model and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across benchmarks, trajectory curvature is reduced by more than 2x, improving generation quality in the few-step regime.
[2606.04092] Optimal Transport Flow Matching by Design
[Submitted on 2 Jun 2026]
Title:Optimal Transport Flow Matching by Design
View a PDF of the paper titled Optimal Transport Flow Matching by Design, by Shimon Malnick and 3 other authors
View PDF HTML (experimental)
Abstract:Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution. When prior-data pairs are coupled via optimal transport (OT), the learned trajectories are straight and non-crossing, enabling fast, even single-step, generation. However, computing the OT coupling in high dimensions is intractable, and existing methods attempt to solve the OT problem, at the cost of persistent bias or significant overhead. Rather than solving for the OT coupling, we reformulate the problem. Once the prior is treated as a design choice rather than a fixed input, the OT coupling between prior and data is no longer unique. Many priors admit an OT-optimal identity coupling to the data, leaving us free to choose one that is also tractable to sample. We identify low-frequency projection of natural images as such a choice. The identity coupling between data and its low-frequency representation is empirically OT-optimal, the prior is structured enough to be sampled by a lightweight model at inference, and the remaining flow-matching task reduces to synthesizing high-frequency detail. Interpolating the prior with Gaussian noise further improves generation quality while preserving the OT coupling. The approach requires no modifications to the flow model itself, and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across all benchmarks, our method reduces trajectory curvature by more than $2\times$ compared to existing flow matching methods, yielding better generation quality in the few-step regime.
Comments: Project page: this https URL
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)
Cite as: arXiv:2606.04092 [cs.CV]
(or arXiv:2606.04092v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2606.04092
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Shimon Malnick [view email] [v1] Tue, 2 Jun 2026 18:00:05 UTC (4,922 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Optimal Transport Flow Matching by Design, by Shimon Malnick and 3 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.CV
new | recent | 2026-06
Change to browse by:
cs cs.LG
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)