A comprehensive numerical study of collisional ripple diffusion of hot ions is performed based upon a well-established banana tip map in a tokamak plasma. New nonlinear resonances are found at inverse-integer harmonics, in addition to the well-known integer number harmonics. It is found that the new nonlinear resonances, when they exist in multiple harmonic numbers, significantly enhance the global collisional diffusion rate in the transition region between the collisional and stochastic diffusion regimes. Much below the stochastic diffusion regime, although the localized collisional ripple diffusion rate at isolated precessional resonances is found to be significantly faster than the previously known rates, its contribution to the radially averaged diffusion is negligible, to reproduce a previously known analytic rate [P. N. Yushmanov, Nucl. Fusion 23, 1599 (1983)]. A simple unified analytic formula to model collisional, transitional and stochastic ripple diffusion rates is suggested. (C) 2003 American Institute of Physics.