  Diffusion is a commonly used technique for spreading information from point
to point on a graph. The rationale behind diffusion is not clear. And the
multi-types Galton-Watson forest is a random model of population growth without
space or any other resource constraints. In this paper, we use the degenerated
multi-types Galton-Watson forest (MGWF) to interpret the diffusion process and
establish an equivalent relationship between them. With the two-phase setting
of the MGWF, one can interpret the diffusion process and the Google PageRank
system explicitly. It also improves the convergence behaviour of the iterative
diffusion process and Google PageRank system. We validate the proposal by
experiment while providing new research directions.
