Flow Matching on Symmetric Spaces
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914530868592640 |
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| author | Ruscelli, Francesco Zanchetta, Ferdinando Fioresi, Rita |
| author_facet | Ruscelli, Francesco Zanchetta, Ferdinando Fioresi, Rita |
| contents | We introduce a general framework for training flow matching models on Riemannian symmetric spaces, 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 greatly simplifying the handling of geodesics. As an application, we showcase our framework on the real Grassmannians $\operatorname{SO}(n) / \operatorname{SO}(k) \times \operatorname{SO}(n-k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03588 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flow Matching on Symmetric Spaces Ruscelli, Francesco Zanchetta, Ferdinando Fioresi, Rita Machine Learning Artificial Intelligence 68T07 We introduce a general framework for training flow matching models on Riemannian symmetric spaces, 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 greatly simplifying the handling of geodesics. As an application, we showcase our framework on the real Grassmannians $\operatorname{SO}(n) / \operatorname{SO}(k) \times \operatorname{SO}(n-k)$. |
| title | Flow Matching on Symmetric Spaces |
| topic | Machine Learning Artificial Intelligence 68T07 |
| url | https://arxiv.org/abs/2605.03588 |