The oxygen diffusion rate in hafnia (HfO2)-based resistive memory plays a pivotal role in enabling nonvolatile data retention. However, the information retention times obtained in HfO2 resistive memory devices are many times higher than the expected values obtained from oxygen diffusion measurements in HfO2 materials. In this study, we resolve this discrepancy by conducting oxygen isotope tracer diffusion measurements in amorphous hafnia (a-HfO2) thin films. Our results show that the oxygen tracer diffusion in amorphous HfO2 films is orders of magnitude lower than that of previous measurements on monoclinic hafnia (m-HfO2) pellets. Moreover, oxygen tracer diffusion is much lower in denser a-HfO2 films deposited by atomic layer deposition (ALD) than in less dense a-HfO2 films deposited by sputtering. The ALD films yield similar oxygen diffusion times as experimentally measured device retention times, reconciling this discrepancy between oxygen diffusion and retention time measurements. More broadly, our work shows how processing conditions can be used to control oxygen transport characteristics in amorphous materials without long-range crystal order.