A device for processing milk foam for use in an automatic hot and/or cold beverage machine includes a milk pump to pump the milk foam, and a secondary processing device coupled to the milk foam pump to change the consistency of the milk foam. The secondary processing device includes a homogenizer to break up and distribute air bubbles in the milk foam. The homogenizer has a reducing region including a plurality of impact bodies arranged to define a channel labyrinth through which the milk foam is flowable. Additionally, there is provided a process for homogenizing milk foam utilizing the above device, includes steps of a) impacting divided partial flows of the milk foam with the impact surfaces to divide the air bubbles of the milk foam and b) mixing the divided partial flows with the divided air bubbles together to form new partial flows.