Through the combination of density functional theory calculations and ab initio atomistic thermodynamics modeling, we demonstrate that atomically dispersed platinum species on ceria can adopt a range of local coordination configurations and oxidation states that depend on the surface structure and environmental conditions. Unsaturated oxygen atoms on ceria surfaces play the leading role in stabilization of PtO_x species. Any mono-dispersed Pt⁰ species are thermodynamically unstable compared to bulk platinum, and oxidation of Pt⁰ to Pt²⁺ or Pt⁴⁺ is necessary to stabilize mono-dispersed platinum atoms. Reduction to Pt⁰ leads to sintering. Both Pt²⁺ and Pt⁴⁺ prefer to form the square-planar [PtO₄] configuration. The two most stable Pt²⁺ species on the (223) and (112) surfaces are thermodynamically favorable between 300 and 1200 K. The most stable Pt⁴⁺ species on the (100) surface tends to desorb from the surface as gas phase above 950 K. The resulting phase diagrams of the atomically dispersed platinum in PtO_x clusters on various ceria surfaces under a range of experimentally relevant conditions can be used to predict dynamic restructuring of atomically dispersed platinum catalysts and design new catalysts with engineered properties.