In these experiments, a few bilayers of D2O were vapor-deposited on a pure crystalline H2O ice film or an ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the D2O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the HDO from the initial HDO mixture layer to HDO isolated in the H2O ice film. This was possible because isolated HDO in H2O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H2O ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations up to 1 x 10(-4) mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) x 10(-4) mole fraction HCl with a concentration-independent rate constant. The diffusion under these conditions followed Arrhenius behavior for T = 135-145 K yielding E-a = 25 +/- 5 kJ/ mol. The mechanism for the HDO diffusion involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop and orientational turn steps. While these spectroscopic results compare favorably with recent studies of molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A comparison and discussion of the various diffusion studies are included in this report.