We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulations. An external pressure restricts local motions of a single molecule within its cage and triggers slowing down of cooperative mobility. While the ECNLE theory and simulations generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulations indicate a decrease of fragility as pressures above 1000 bar. The structural relaxation time is found to be linearly coupled with the inverse diffusion constant. Remarkably, this coupling is independent of compression. The theoretical calculations quantitatively agree well with the simulations and are also consistent with prior work.