The diffusion statistics of atoms in a crystal close to the critical superheating temperature was studied in detail using molecular dynamics and Monte Carlo simulations. We present a continuous random-walk model for diffusion of atoms hopping through thermal vacancies. The results obtained from our model suggest that the limit of superheating is precisely the temperature for which dynamic percolation happens at the time scale of a single individual jump. A possible connection between the critical superheating limit and the maximization of the Shannon entropy associated with the distribution of jumps is suggested. As a practical application of our results, we show that an extrapolation of the critical superheating temperature (and therefore an estimation of the melting point) can be performed using only the dynamical properties of the solid state.