Stable Autonomous Flow Matching
Christopher Iliffe Sprague Arne Elofsson Hossein Azizpour
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.