A space-saving vibration damper that functions reliably for a long term. The vibration damper has a housing that includes at least one concave recess which is sealed by a disk-shaped diaphragm comprising a spring steel sheet. The diaphragm is connected by its edge to a planar surface of the housing by means of material-to-material bonding. The housing has, at the edge of the recess, a rounding that changes over continuously into both the recess and the planar housing surface toward the diaphragm. The hollow chamber disposed between the diaphragm and the recess is filled with air. The vibration damper is designed for use in slip-controlled hydraulic brake systems for a vehicle.