Recent ground-based and spacecraft observations of comets in the inner solar system reveal two distinct features that provide important insight into their origin and evolution. The first of these is the observation that the D/H ratio of water vapor in cometary comae is significantly higher than that in Vienna Standard Mean Ocean Water (VSMOW). The second observation is that cometary jets are bursty (i.e, roughly steady state emissions that are punctuated with short-lived outbursts of water vapor and other materials) (Hughes, 1990; Soderblom et al., 2002; Soderblom et al., 2004a; Soderblom et al., 2004b). We present an experimental and theoretical study of ice sublimation in a vacuum that reveals several heretofore unknown and fundamental characteristics about the kinetics and mechanisms of ice sublimation that may explain both of these observed phenomena. In particular, we observe quasi-periodic sublimation cascades on time scales of hours to days, the D/H ratio in the vapor issuing from the sample is in general different from that of the sample, and in many cases, quasi-periodic changes in the D/H ratio of the vapor accompany the sublimation cascades. Changes are also observed in the infrared spectrum of the sample before, during and after a cascade that are consistent with our hypothesis that vacuum sublimation of water ice is a diffusive process that works to leave behind the most strongly bound molecules. Finally, we speculate as to whether the effects observed in the lab can be extrapolated to cometary-nucleus-scale phenomena.