A self-priming centrifugal pump comprises an inlet and an outlet, and a centrifugal impeller for receiving liquid from the inlet and delivering it to the outlet. An inlet valve and an outlet valve are provided, and a diaphragm arrangement is driven by the same motor as the impeller to provide priming. The diaphragm arrangement can be integrated into a pump design without taking up significant additional space. By driving the diaphragm arrangement with the motor, no additional power source is required.