Recently, angle-resolved photoemission spectroscopy has been used to highlight an anomalously large band renormalization at high binding energies in cuprate superconductors: the high energy waterfall or high energy anomaly (HEA). The anomaly is present for both hole- and electron-doped cuprates as well as the half-filled parent insulators with different energy scales arising on either side of the phase diagram. While photoemission matrix elements clearly play a role in changing the aesthetic appearance of the band dispersion, i.e. creating a waterfall-like appearance, they provide an inadequate description for the physics that underlies the strong band renormalization giving rise to the HEA. Model calculations of the single-band Hubbard Hamiltonian showcase the role played by correlations in the formation of the HEA and uncover significant differences in the HEA energy scale for hole- and electron-doped cuprates. In addition, this approach properly captures the transfer of spectral weight accompanying doping in a correlated material and provides a unifying description of the HEA across both sides of the cuprate phase diagram. We find that the anomaly demarcates a transition, or cross-over, from a quasiparticle band at low binding energies near the Fermi level to valence bands at higher binding energy, assumed to be of strong oxygen character. Show Partial Abstract