Deep Inelastic Neutron Scattering (Neutron Compton Scattering), is used to measure the momentum distribution of the protons in water from temperatures slightly below freezing to the supercritical phase. The momentum distribution is determined almost entirely by quantum localization effects, and hence is a sensitive probe of the local environment of the proton. The distribution shows dramatic changes as the hydrogen bond network becomes more disordered. Within a single particle interpretation, the proton moves from an essentially harmonic well in ice to a slightly anharmonic well in room temperature water, to a deeply anharmonic potential in the supercritical phase that is best described by a double well potential with a separation of the we...