We present a study of the first stages of growth of thin films produced by low-energy cluster beam deposition (LECBD) on graphite. Our experiments are analyzed in the framework of new models including three physical ingredients, which are the deposition, the diffusion and the aggregation of the clusters. The comparison between computer simulations of the model and the experimental structures reveals that only the incident clusters diffuse on the graphite, the dusters stick irreversibly upon contact, and allow us to quantify the diffusion of clusters on graphite. Two kinds of metallic cluster films are studied: thin films produced by deposition of antimony clusters (containing 2300 and 250 atoms) and others by deposition of gold clusters (containing about 250 atoms). In both cases, we find that the clusters, in spite of their large size, diffuse very rapidly on the surface. The different microscopic diffusion mechanisms proposed in the literature are investigated, but none is compatible with our experimental results. Finally, we suggest a collective mechanism where the cluster rotates on the surface as a rigid entity to explain our results.