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Manifold-Stable Flow Matching — arXiv:2609.35454

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.35454
License (as archived): CC0-1.0
Archived: 2026-10-07T22:39:08.203Z
SHA-256 of the archived text: c67ea39bfd7576ad7917396831d81409a654931266586e7577359b91692b6b62
Stable URL of this page: https://metraipolis.com/documento/dc_eb0ce2b13dcc

How to cite

Manifold-Stable Flow Matching — arXiv:2609.35454 — arXiv (en), https://arxiv.org/abs/2609.35454 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eb0ce2b13dcc (Metraipolis archive dc_eb0ce2b13dcc, sha256 c67ea39bfd7576ad7917396831d81409a654931266586e7577359b91692b6b62)

BibTeX

@misc{dceb0ce2b13dcc,
  title = {Manifold-Stable Flow Matching — arXiv:2609.35454},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.35454},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eb0ce2b13dcc; sha256 c67ea39bfd7576ad7917396831d81409a654931266586e7577359b91692b6b62},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.35454. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order $10^{-6}$. In Push-T robotic experiments, MSFM raises success from $74\%$ to $82\%$. In the Robomimic Square task, success increases from $60\%$ to $72\%$, while rotation-manifold deviation decreases from order $10^{-2}$ to $10^{-7}$. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-29 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Robotics (cs.RO); Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2609.35454 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T22:14:28.443Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).