A continuous process for making a pigment dispersion includes continuously feeding a pigment into a feed section of a screw extruder at a controlled rate, continuously feeding a surfactant into the feed section of the screw extruder at a controlled rate, continuously feeding water downstream of the feed section to emulsify the pigment and the surfactant, forming a water-in-pigment dispersion, continuously feeding additional water downstream of the previously fed water to cause a phase inversion of the water-in-pigment dispersion, forming a pigment-in-water dispersion, continuously homogenizing the pigment-in-water dispersion in the screw extruder to create a homogenous aqueous pigment dispersion and collecting the homogenous aqueous pigment dispersion from an exit section of the screw extruder.