A systematic experimental investigation of capillary pressure characteristics and fluid flow in diatomite was begun. Using an X-ray CT scanner and a specially constructed imbibition cell, we study spontaneous water imbibition processes in diatomite and, for reference, Berea sandstone and chalk. The mass of water imbibed as a function of time is also measured. Imbibition is restricted to concurrent flow. Despite a marked difference in rock properties such as permeability and porosity, we find similar trends in saturation profiles and weight gain versus time functions. Imbibition in diatomote is relatively rapid when initial water saturation is low due to large capillary forces. Using a non-linear regression analysis together with the experimental data, the capillary pressure and water relative permeability curves are determined for the diatomite in the water-air system. The results given for displacement profiles by numerical simulation match the experimental results.