The behaviors of molecular self-diffusion were simulated in complex spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings in liquid nuclear magnetic resonance (NMR). The simulation algorithm was based on a combination of the non-linear Bloch equations, product operator matrix, and finite difference method. The simulated results reveal different diffusion behaviors of inter- and intra-molecular multiple-quantum coherences, coincident with theoretical predictions and experimental measurements. Compared with the Monte Carlo method, the finite difference method is more precise and efficient for simulating diffusion behaviors of multiple-quantum coherences. (c) 2005 Elsevier B.V. All rights reserved.