The diode effect is fundamental to electronic devices and is widely used in rectifiers and a.c.-d.c. converters. At low temperatures, however, conventional semiconductor diodes possess a high resistivity, which yields energy loss and heating during operation. The superconducting diode effect (SDE)1-8, which relies on broken inversion symmetry in a superconductor, may mitigate this obstacle: in one direction, a zero-resistance supercurrent can flow through the diode, but for the opposite direction of current flow, the device enters the normal state with ohmic resistance. The application of a magnetic field can induce SDE in Nb/V/Ta superlattices with a polar structure1,2, in superconducting devices with asymmetric patterning of pinning centres9 or in superconductor/ferromagnet hybrid devices with induced vortices10,11. The need for an external magnetic field limits their practical application. Recently, a field-free SDE was observed in a NbSe2/Nb3Br8/NbSe2 junction; it originates from asymmetric Josephson tunnelling that is induced by the Nb3Br8 barrier and the associated NbSe2/Nb3Br8 interfaces12. Here, we present another implementation of zero-field SDE using noncentrosymmetric [Nb/V/Co/V/Ta]20 multilayers. The magnetic layers provide the necessary symmetry breaking, and we can tune the SDE by adjusting the structural parameters, such as the constituent elements, film thickness, stacking order and number of repetitions. We control the polarity of the SDE through the magnetization direction of the ferromagnetic layers. Artificially stacked structures13-18, such as the one used in this work, are of particular interest as they are compatible with microfabrication techniques and can be integrated with devices such as Josephson junctions19-22. Energy-loss-free SDEs as presented in this work may therefore enable novel non-volatile memories and logic circuits with ultralow power consumption.