  This paper presents a novel approach to generating stabilizing controllers
for a large class of dynamical systems using diffusion models. The core
objective is to develop stabilizing control functions by identifying the
closest asymptotically stable vector field relative to a predetermined manifold
and adjusting the control function based on this finding. To achieve this, we
employ a diffusion model trained on pairs consisting of asymptotically stable
vector fields and their corresponding Lyapunov functions. Our numerical results
demonstrate that this pre-trained model can achieve stabilization over
previously unseen systems efficiently and rapidly, showcasing the potential of
our approach in fast zero-shot control and generalizability.
