  The diffusion of atoms and radicals on interstellar dust grains is a
fundamental ingredient for predicting accurate molecular abundances in
astronomical environments. Quantitative values of diffusivity and diffusion
barriers usually rely heavily on empirical rules. In this paper, we compute the
diffusion coefficients of adsorbed nitrogen atoms by combining machine-learned
interatomic potentials, metadynamics, and kinetic Monte Carlo simulations. With
this approach, we obtain a diffusion coefficient of nitrogen atoms on the
surface of amorphous solid water of merely $(3.5 \pm
1.1)10^{-34}$cm$^2$s$^{-1}$ at 10 K for a bare ice surface. Thus, we find that
nitrogen, as a paradigmatic case for light and weakly bound adsorbates, is
unable to diffuse on bare amorphous solid water at 10 K. Surface coverage has a
strong effect on the diffusion coefficient by modulating its value over 9--12
orders of magnitude at 10 K and enables diffusion for specific conditions. In
addition, we have found that atom tunneling has a negligible effect. Average
diffusion barriers of the potential energy surface (2.56 kJ mol$^{-1}$) differ
strongly from the effective diffusion barrier obtained from the diffusion
coefficient for a bare surface (6.06 kJ mol$^{-1}$) and are, thus,
inappropriate for diffusion modeling. Our findings suggest that the thermal
diffusion of N on water ice is a process that is highly dependent on the
physical conditions of the ice.
