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Stable Autonomous Flow Matching
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Stable Autonomous Flow Matching
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In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.
Forward citations
Cited by 3 Pith papers
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Let the Dynamics Flow: Stable Flow Matching Dynamical Systems
SFMDS parametrizes dynamical systems via flow matching with soft penalty or hard architectural constraints to enforce stability while preserving multimodality, extended to Lie groups.
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Let the Dynamics Flow: Stable Flow Matching Dynamical Systems
SFMDS learns multimodal dynamical systems via flow matching under soft or hard Lyapunov/positive-invariance constraints, including on Lie groups, and reports stable robot motion generation.
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Energy Generative Modeling: A Lyapunov-based Energy Matching Perspective
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite...
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