Valence band of a vacuum-reduced $TiO_2$ (001) surface has been carefully examined using synchrotron x-ray photoelectron spectroscopy to investigate variation of the gap state upon oxidation and thermal diffusion of $Ti^{3+}$ interstitials from the bulk. We compare our results with that obtained from $TiO_2$ (110) and aim to address a crystal-face dependency in the oxidation and diffusion rates of $Ti^{3+}$ interstitials. We find very similar behaviors in the oxidation and thermal diffusion rate of $Ti^{3+}$ interstitials between the two crystal faces suggesting a negligible crystal-face dependency in this case.