A pump comprising a support-forming assembly for securing to a receptacle containing a substance to be dispensed, a moving member co-operating with the support-forming assembly to define a pump chamber of variable volume, and an elastically deformable diaphragm secured to one of the support-forming assembly and the moving member, the diaphragm being arranged so as to deform elastically when the moving member is displaced relative to the support, the pump further comprising a suction valve-forming element arranged to oppose any return of substance towards the receptacle while the volume of the pump chamber is decreasing, and a delivery valve-forming element arranged to oppose any entry of air into the receptacle while the volume of the pump chamber is increasing. The delivery valve-forming element is made by means of a shutter-forming element that is separate from the diaphragm.