Abstract: The dispenser is adapted to dispense different size cups, such as portion cups, and includes a housing for storing a plurality of cups in a nested stack and a flexible diaphragm covering the discharge end of the housing. The diaphragm includes a web section having a central discharge opening through which the bottom of the outermost cup of the stack extends to be grasped and withdrawn from the stack. The discharge opening preferably has a symmetrical polygonal shape, such as a hexagonal shape, and has an inner periphery configured to retain a stack of the smallest cups to be dispensed in the housing while permitting the outermost cup in the stack to be drawn from the housing.