Structural changes during annealing of high-density amorphous ice were studied with both neutron and x-ray diffraction. The first diffraction peak was followed from the high- to the low-density amorphous form. Changes were observed to occur through a series of intermediate forms that appear to be metastable at each anneal temperature. Five distinct amorphous forms were studied with neutron scattering, and many more forms may be possible. Radial distribution functions indicate that the structure evolves systematically between 4 and 8 angstroms. The phase transformations in low-temperature liquid water may be much more complex than currently understood.