Experimental inelastic cross section data are used to successfully recover the diabatic coupling potential for the C4+ +He system via a general iterative inversion algorithm based on first-order functional sensitivity analysis and Tikhonov regularization, The coupling potential was found to converge to a curve with a distinctly different shape from that of an earlier fitted-parameter model potential. Grass sections calculated from the new potential reproduce the relative heights and shapes of the peaks in the experimental cross sections much better than those obtained from the parametrized potential.