We investigate the dynamics of interfaces growth in inhomogeneous systems. The description of the kinetics is based on the mean field master equation in terms of lattice gas model. The existence of repulsive interactions between nearest-neighbour particles creates an order in the system. We show that the order extension has an influence on the localisation of the diffusive interface called "the diffusion front" which delimits disordered region from ordered one. We analyze the time evolution of diffusion fronts by dynamic scaling approach and we find that the scaling behavior of these interfaces is characterized by anomalously large exponents which agree with the experimental and theoretical results.