A generator for a wind turbine is disclosed. The generator comprises a rotor configured to rotate about a rotational axis, and at least one stator arranged next to the rotor. Each stator comprises at least one flux-generating module facing the rotor but spaced therefrom, thereby forming an air gap between the rotor and each flux-generating module. Each stator also comprises at least one bearing unit, each bearing unit comprising a body defining a cavity with an open end facing the rotor. The generator further comprises a source of pressurized fluid communicating with each bearing unit, and the body of each bearing unit directs the fluid towards the rotor to help maintain the air gap between the rotor and each flux-generating module. Thereby the air gap between the rotor and the flux-generating modules is controlled by means of the fluid bearing units. The invention further provides a wind turbine comprising such a generator.