A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely separated time scales, a set of three equations is derived for the fast degree of freedom, the slow degree of freedom, and the coupling between these two hierarchies. It is shown that this approach consistently describes "diffusing diffusivity" and non-Gaussian normal diffusion.