In recent years a model for predicting sound fields in enclosures has been proposed, based on the mathematical theory of diffusion. This model is held to be valid for predicting the late reverberation component of the impulse response, on the basis that sufficient reflection events must occur [Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)]. The present work determines numerically the extent of reflections necessary for the solution of the diffusion equation model to be accurate in quasi-cubic rooms. Some preliminary numerical experiments have been carried out to determine after how many mean-free times of the impulse response, which is obtained by a geometrical-acoustic approach, gives a similar result to the solution obtained from a diffusion equation model.