The relationship between the acoustic scattering characteristics of materials and the degree of diffusion in enclosed acoustic spaces has recently attracted considerable research attention. Hanyu [J. Acoust. Soc. Am. 128(3), 1140-1148 (2010)] introduced a theoretical framework, in which the diffusion time in an enclosure is expressed as a function of a material's average scattering coefficient. In this letter, a modification of this theory is proposed. The decay process of the sound energy through scattering is divided into discrete sub-processes, specifically, a purely scattering process, and alternating scattering and specular reflections. The behavior of each process is examined for different scattering coefficients.