The diffusion properties of overdamped particles moving in spatially symmetrical periodic potentials subject to both symmetrical time-periodic driving and stochastic forcing are investigated [the typical model formally reads $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{x}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}V}^{\ensuremath{'}}(x)+U(t)+\ensuremath{\gamma}(t)$, $V(L\ifmmode\pm\else\textpm\fi{}x)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}V(x)$, $U(T+t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}U(t)$, $〈\ensuremath{\gamma}(t)〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, $〈\ensuremath{\gamma}(t)\ensuremath{\gamma}(\ensuremath{\tau})〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2D\ensuremath{\delta}(t\ensuremath{-}\ensuremath{\tau})$]. It is found that the diffusion rate can be greatly enhanced if the various forcings are chosen in an optimal matching. In particular, we may get a diffusion rate larger than the rate of free diffusion.