Flow matching on homogeneous spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910073702318080 |
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| author | Ruscelli, Francesco |
| author_facet | Ruscelli, Francesco |
| contents | We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This strategy avoids the potentially complicated geometry of homogeneous spaces by working directly on Lie groups, which in turn enables us reduce the problem to a Euclidean flow matching task on Lie algebras. In contrast to Riemannian Flow Matching, our method eliminates the need to define and compute premetrics or geodesics, resulting in a simpler, faster, and fully intrinsic framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24829 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flow matching on homogeneous spaces Ruscelli, Francesco Machine Learning 68T07 We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This strategy avoids the potentially complicated geometry of homogeneous spaces by working directly on Lie groups, which in turn enables us reduce the problem to a Euclidean flow matching task on Lie algebras. In contrast to Riemannian Flow Matching, our method eliminates the need to define and compute premetrics or geodesics, resulting in a simpler, faster, and fully intrinsic framework. |
| title | Flow matching on homogeneous spaces |
| topic | Machine Learning 68T07 |
| url | https://arxiv.org/abs/2603.24829 |