  Surface diffusion on metal oxides is key in many areas of materials
technology, yet it has been scarcely explored at the atomic scale. This work
provides phenomenological insights from scanning tunneling microscopy on the
link between surface diffusion, surface atomic structure, and oxygen chemical
potential based on three model oxide surfaces: Fe$_2$O$_3(1\overline{1}02)$,
La$_{1-x}$Sr$_x$MnO$_3$(110), and In$_2$O$_3$(111). In all instances, changing
the oxygen chemical potential used for annealing stabilizes reconstructions of
different compositions while promoting the flattening of the surface morphology
-- a sign of enhanced surface diffusion. It is argued that thermodynamics,
rather than kinetics, rules surface diffusion under these conditions: The
composition change of the surface reconstructions formed at differently
oxidizing conditions drives mass transport across the surface.
