This paper deals with the construction of approximate series solutions of diffusion models with stochastic excita- tion and nonlinear losses using the homotopy analysis method (HAM). The mean, variance and other statistical properties of the stochastic solution are computed. The solution technique was applied successfully to the 1D and 2D diffusion models. The scheme shows importance of choice of convergence-control parameter ħ to guarantee the convergence of the solutions of nonlinear differential Equations. The results are compared with the Wien- er-Hermite expansion with perturbation (WHEP) technique and good agreements are obtained.