The propagation of a dust-ion-acoustic wave (DIAW) wave down the steep density gradient in an inhomogeneous diffusive dusty plasma is experimentally studied. It is observed that the presence of the dust enhances the plasma inhomogeneity. The phase velocity of the DIAW increases rapidly with distance and becomes supersonic. The interplay between the effects of the density nonuniformity and collisional damping results in the continuous transition of the relative amplitude of the DIAW from damping to growth. The experimental data are in agreement with theoretical prediction and confirm the importance of density-dependent ion-dust collisions. (C) 2001 American Institute of Physics.