Thin poly(styrene-block-p-methylstyrene) diblock copolymer films on top of silicon substrates were examined right after preparation and during the early stages of annealing. Using specular and off-specular X-ray scattering as well as scanning force microscopy, the film morphology is determined. With the spin-coating technique films are prepared which exhibit a roughness correlation between the substrate and the copolymer surface within a limited film thickness and molecular weight range right after preparation. The transferred part of the roughness spectrum of the substrate is probed and explained as a morphology of a frozen liquid with a surface bending rigidity. During annealing the energetically unfavorable roughness replication decays, and an internal ordering is formed. The decay of long-range correlation is explained by a surface diffusion where diffusion is slowed down as compared to bulk behavior.