Cartan flow matching

[2605.03588] Cartan flow matching Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2605.03588 (cs) [Submitted on 5 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Cartan flow matching Authors: Francesco Ruscelli , Ferdinando Zanchetta , Rita Fioresi View PDF HTML (experimental) Abstract: We introduce Cartan flow matching, a general framework for training flow matching models on Riemannian symmetric spaces, i.e. Riemannian manifolds with the property that at any point there exists a geodesic symmetry. This is a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate flow matching on symmetric spaces as flow matching on a subspace of the Lie algebra of their isometry group, thus linearizing the problem and avoiding the need to construct geodesic interpolation paths on the manifold. As an application, we showcase our framework on the real Grassmannians $ \operatorname{SO}(n) / \operatorname{SO}(k) \times \operatorname{SO}(n-k) $. Comments: Major revision. Fixed a mistake in section 4. 14 pages, 1 figure Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) MSC classes: 68T07 Cite as: arXiv:2605.03588 [cs.LG] (or arXiv:2605.03588v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2605.03588 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Francesco Ruscelli [ view email ] [v1] Tue, 5 May 2026 10:03:12 UTC (2,168 KB) [v2] Thu, 27 Aug 2026 07:05:49 UTC (1,142 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2026-05 Change to browse by: cs cs.AI References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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