We consider a nonlinear Schroedinger equation (NLS) with random coefficients, in a regime of separation of scales corresponding to diffusion approximation. Our primary goal is to propose and study an efficient numerical scheme in this framework. We use a pseudo-spectral splitting scheme and we establish the order
of the global error. In particular we show that we can take an integration step larger than the smallest scale of the problem, here the correlation length of the random medium. Then, we study the asymptotic behavior of the numerical solution in the diffusion approximation regime.