Recent experimental chemical vapor depositions of silicon at extreme pressures of ~ 50 MPa (~ 500 atm) have been observed to generate remarkably smooth surfaces not predicted by low-pressure deposition models. In this paper, we propose an anti-shadowing mechanism where the collision of particles within the valleys of the surface growth front leads to smoothening. We conduct Monte Carlo simulations to simulate the evolution of film roughness at pressures between 1 and 50 MPa. We observe that surface roughness approaches an asymptotic invariant value that follows power law behavior as a function of pressure. The film thickness at which invariance begins is shown to have a similar power law behavior with respect to pressure. Our simulated results compare favorably with recent experimental observations and provide insight into the fundamental mechanisms underlying film evolution at pressures between one and hundreds of atmospheres.