Many oxygen-deficient oxide perovskites are oxygen ion conductors in a dry environment. However, in a humid atmosphere, they absorb water to fill up oxygen vacancies, release quasi-free protons into the structure, and thereby become proton conductors. Absorption of water requires the transport of both protons and oxygen ions. This effectively leads to the transport of H2O under its chemical potential gradient. The present manuscript develops relationships between the chemical diffusion coefficient of H2O and the diffusion coefficients of protons and oxygen vacancies with an emphasis on the role of solution thermodynamics.