We use molecular dynamics simulations to investigate the effect of the density of the host material on the isomerization-induced diffusion mechanism that results in surface relief gratings formation. We find that a decrease in density increases the diffusion coefficient in a similar way for driven and spontaneous diffusion. This result suggests that the driving mechanism depends only slightly on the density of the host material. The pressure variations during the isomerization process decrease when the driven diffusion increases due to material softening for smaller densities. These results suggest that the pressure variations are not at the origin of the driven motions. The relative local density variation around the probe is also weakly dependent on the mean density of the host material as long as the material structure is preserved.