We report on our growth of superconducting SmFeAs(O,F) films by F diffusion. In our process, F-free SmFeAsO films were grown by molecular beam epitaxy (MBE) first, and subsequently F was introduced into the films via F diffusion from an overlayer of SmF3. We performed a detailed comparison of the growth conditions and also the properties of resultant films for fluoride and oxide substrates. The best films on CaF2 exhibited a high transition temperature, T
end) = 57.8 K (56.4 K) at highest, which may exceed the highest T
c ever reported for bulk samples. Furthermore the films on CaF2 also showed high critical current density over 1 MA/cm2 in self-field at 5 K.