A machine for making liquid or semi-liquid food products comprises: a frame; a first container containing a liquid or semi-liquid base product; a second container defining a processing chamber for processing a base mixture made up of the liquid or semi-liquid base product and a gas; a stirrer mounted inside the second container; thermal treatment means associated with the second container, acting in conjunction with the stirrer to convert the base mixture inside the second container into a finished liquid or semi-liquid product; a connecting duct connecting the first container to the second container and configured to connect the first container to the second container in such a way as to allow the base mixture to be transferred to the second container; a dispenser connected to the second container to allow dispensing the finished product.