In this contribution, we present a concept for simultaneous filtration and pumping solely realized with a single polymer-based foam membrane. An open-porous foam with a gradient in pore size, which essentially resembles a nozzlediffuser structure, is integrated into the center of a flexible poly(dimethylsiloxane) membrane, which is placed into a small fluid cavity with symmetric inlet and outlet geometry. The actuation of the membrane is achieved with an electromagnetic coil from the outside and a small magnetic ring, which has also been integrated into the membrane. The sinusoidal excitation of the membrane leads to a vibrational movement of the membrane in the fluid cavity, and due to the asymmetry in pore size of the integrated foam and the associated asymmetry in hydrodynamic resistance a unidirectional fluid flow evolves in the system. Thus, the proposed device can be used for simultaneous pumping and filtration with the additional advantage of reduced sensitivity to fouling due to the intrinsic vibration of the membrane.