The generalized Langevin equation for the cooperative dynamics of interacting polymer chains is implemented to investigate the anomalous dynamics of unentangled polymer melts. The proposed equation of motion formally relates the anomalous center-of-mass diffusion, as observed in computer simulations and experiments, to the nature of the effective intermolecular mean-force potential. An analytical Gaussian-core form of the potential between the centers of mass of two polymers is derived, which agrees with computer simulations and allows the analytical solution of the equation of motion. The calculated center-of-mass dynamics is characterized by an initial subdiffusive regime that persists for the spatial range of the intermolecular mean-force potential and for time intervals shorter than the first intramolecular relaxation time, in agreement with experiments and computer simulations of unentangled polymer melt dynamics.