A heat pump system includes a caloric heat pump with a regenerator housing that is rotatable about an axial direction. A caloric material is disposed within a chamber of the regenerator housing. The caloric material defines a plurality of channels that extend along the axial direction through the caloric material. The channels of the plurality of channels are spaced from one another along a circumferential direction within the caloric material. A working fluid is flowable through the plurality of channels between end portions of the regenerator housing. A related refrigerator appliance is also provided.