In a hydraulic fluid pump, in particular for a vehicle brake system, having a housing and a piston that is mounted in an axially movable manner in the housing in a piston chamber. A drive moves the piston and a sealing element seals off the piston chamber in the direction of the drive. The sealing element is designed as a diaphragm that extends through the piston chamber transversely with respect to the movement direction of the piston.