The intermediate vibrational energy regime-well above the zero point, yet below the first dissociation limit-plays an important role in many molecular processes, such as radiationless transitions or intramolecular vibrational energy redistribution (IVR). For molecules with N>6 vibrational degrees of freedom, the calculation of energy levels and spectra of the full anharmonic vibrational Hamiltonian at high energies presents a formidable problem. Here we derive an asymptotic factorization of the potential energy surface (PES) based on the global topography of molecular potentials. The resulting approximate models require only a few input parameters such as vibrational frequencies and cubic anharmonicities. They are compared to benchmark PES derived from curvilinear model potentials and Monte Carlo sampled ab initio calculations for several small molecules. Higher order couplings are found to make a significant contribution to IVR decays at long times.