Incorporating Stability Into Flow Matching

Christopher Iliffe Sprague, Arne Elofsson, Hossein Azizpour

Keywords: flow matching, generative modeling, stability theory, dynamical systems

TL;DR: In this paper, we apply a stochastic version of La Salle's invariance principle to flow matching models for data that describes physically stable states.

Abstract: 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 to flow matching models. In doing so, we formally characterize a 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 a toy example.

Submission Number: 149