{"ID":3004716,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T11:43:53.432517148Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03834","arxiv_id":"2606.03834","title":"Let the Dynamics Flow: Stable Flow Matching Dynamical Systems","abstract":"Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, incorporating formal stability guarantees into these generative models, a prerequisite to ensure safe and generalizable robot behaviors, remains a significant challenge. While modeling robot motions as dynamical systems allows for such stability-based inductive biases, existing frameworks struggle to capture the rich action distributions inherent in complex robotic tasks. This paper introduces Stable Flow Matching Dynamical Systems (SFMDS), a novel framework that bridges the gap between high-capacity generative modeling and formal Lyapunov stability guarantees. SFMDS parametrizes dynamical systems via flow matching while simultaneously constraining the model to a family of stable solutions. We propose two variants: a soft constraint based on a penalty term, and a hard structural constraint embedded directly in the model architecture. We further extend both formulations to Lie groups. Experiments on benchmark datasets, in simulation, and on a humanoid robot show that SFMDS learns stable, scalable, and multimodal dynamical systems in low- and high-dimensional state spaces, enabling safe and expressive robot motion generation.","short_abstract":"Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, incorporating formal stability guarantees into these generative models, a prerequisite to ensure safe and generalizable robot behaviors, remains a significant challen...","url_abs":"https://arxiv.org/abs/2606.03834","url_pdf":"https://arxiv.org/pdf/2606.03834v1","authors":"[\"Rodrigo Pérez-Dattari\",\"Francisco Leiva\",\"Andrea Testa\",\"Leonel Rozo\",\"Javier Ruiz del Solar\",\"Noémie Jaquier\"]","published":"2026-06-02T16:17:26Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}