Protein structure prediction has become increasingly popular and successful in recent years. An essential step for fragment-free, template-free methods is the generation of a final three-dimensional protein model from a set of predicted amino acid contacts that are often described by interresidue pairwise atomic distances. Here we explore the use of modern, open-source molecular dynamics (MD) engines, which have been continually developed over the last three decades with all-atom Hamiltonians to model biomolecular structure and dynamics, to generate accurate protein structures starting from a set of inferred pairwise distances. Additionally, the ability of MD empirical physical potentials to correct inaccuracies in the predicted geometries is tested. We rigorously characterize the effect of modeling parameters on results, the effect of different amounts of error in the predicted distances on the final structures, and test the ability of post-processing analysis to sort the best models out of a set of statistical replicas. We find that with exact distances and with noisy distances, the method can produce excellent structural models, and that the molecular dynamics force field seems to help correct errors in distance predictions, resisting the effects of applied noise.