In this note, we investigate almost sure exponential stability for a class of switching diffusion processes. Lyapunov type sufficient conditions to ensure this type of stability for nonlinear switching diffusions are derived. The conditions are an improvement over related results in the literature, since they do not rely on the moment stability of the system. These conditions are then specialized to case of linear switching diffusion processes, to provide easily checkable sufficient criteria for exponential stabilization and robust stability.