Various embodiments provide a flow forming apparatus including: a lathe, the lathe having a base body including a machine bed and a headstock connected to the machine bed, a chuck supported by the headstock, and a mandrel configured to receive a workpiece, with the mandrel having a longitudinal axis and being supported by the headstock; and a build-up system, the build-up system including: a roller head structure having a movably supported roller housing supporting a roller, with the roller being configured to act on the workpiece when the workpiece is received by the mandrel; an axial feeder configured to drive the roller head structure in the axial direction of the longitudinal axis of the mandrel; a radial feeder configured to drive the at least one moveably supported roller housing in the radial direction of the longitudinal axis of the mandrel; and a frame, the frame supporting the roller head structure and the axial feeder; wherein the build-up system is a system separated from the lathe, wherein the machine bed supports the frame, and wherein the frame is fixed to the lathe.