Real-space geometric curvature in magnetic thin films introduces a controllable mechanism for tailoring the pathways of superconducting steady-state Josephson currents via the proximity effect. We present a generalized Green’s function method for calculating diffusive transport in arbitrarily curved surfaces, and show how the competing mechanisms of curvature and distance regulate conversion between different superconducting pairings in a proximity-coupled ferromagnet. We show how this dictates the distribution of current density, with the possibility of curvature-controlled current density manipulation, induced eddy currents and current reversal.