We present two-dimensional (2D) infrared (IR) spectra of isotope diluted ice in its low density amorphous form. Amorphous ice, which is structurally more similar to liquid water than to crystalline ice, provides higher resolution spectra of the hydrogen bond potentials because all motion is frozen. In the case of OD vibration of HOD in H2O, diagonal and off-diagonal (intermode) anharmonicity as well as the relaxation rate of the first excited state increase with hydrogen bond strength in a consistent way. For the OH vibration of HOD in D2O, additional more specific couplings need to be taken into account to explain the 2D IR response, that is, a Fermi resonance with the HOD bend vibration and couplings to phonon modes that lead to quantum beating. The lifetime of the fist excited state, 240 fs, is the shortest ever reported for any phase of isotope diluted water.