We present an iterative predictor-corrector technique designed to derive transferable interatomic potentials from experimental X-ray or neutron scattering measurements of monoatomic liquids. The Structure-Optimized Potential Refinement (SOPR) approach is supported by structure-potential uniqueness theorems for monoatomic dense fluids, and experimental and simulation uncertainties are smoothed via non-parametric Gaussian process regression. We initially apply the technique to noble liquids (Ne, Ar, Kr, Xe), but the results are expected to be generalizable to other monatomic and molecular liquids. Interatomic potentials were obtained using experimental scattering measurements at a single state where only knowledge of the density and a starting reference potential are required to initiate the method. Transferability of the obtained potentials is demonstrated by predicting vapor liquid equilibrium over a range of states with acceptable accuracy from the triple to the critical point for the test fluids. The results reveal that experimental scattering results provide crucial insight into interatomic forces at a length scale complimentary to atomistic or quantum mechanical simulation techniques. Furthermore, the transferable potentials obtained using SOPR demonstrate that scattering experiments may be utilized to predict thermodynamic properties in physical systems where experimental data is unavailable or impractical to obtain.