We have presented a first principles theoretical study of vibrational spectral diffusion and underlying molecular dynamics in supercritical heavy water at three different densities ranging from 1.1 to 0.39 g cm(-3). Our calculations are based on ab initio molecular dynamics simulations for trajectory generation and wavelet analysis for frequency calculations, and no empirical potential parameters are involved in the present study. Calculations of OD frequency-distance (D center dot center dot center dot O) conditional probabilities reveal that the rate of increase of OD frequency with D center dot center dot center dot O distance gradually decreases with lowering of density. Also, the maximum probability moves to a higher frequency-larger D center dot center dot center dot O distance region with decreasing density due to weakening of hydrogen bonds and increased number of dangling OD bonds in these systems. The correlations between the stretch frequencies and the electric fields on D atoms (along OD bonds) are also calculated, and the magnitude of such correlations is found to be similar to those of frequency-distance (D center dot center dot center dot O) correlations for the present supercritical systems. The vibrational spectral diffusion in supercritical water shows two time scales: one around 100 fs or less and the other in the region of 150-600 fs with the shorter time scale carrying the larger weight. It is found that, unlike ambient water, for supercritical water the slower component of the spectral diffusion does not necessarily capture the hydrogen bond dynamics at all densities. Rather, an interplay between the dynamics of hydrogen bonds, dangling OD groups, and the inertial rotation of OD bonds determines the times scales of spectral diffusion in a rather subtle manner. While the slower component of spectral diffusion at high density is determined by the lifetimes of hydrogen bonds, it is the lifetime of dangling OD groups that decides the slower component at low density, and the reverse holds for the faster components. The fast inertial rotation also shows up as the faster component of spectral diffusion. Dynamical correlations between the relaxation of frequency fluctuations and that of electric field fluctuations are also explored. Our calculations of rotational dynamics show, unlike ambient water, no frequency dependence of the rotational relaxation of OD bonds because of faster interconversion of different hydrogen bonding states and a reduced role of the hydrogen bond strength as a significant determinant of rotational motion caused by higher thermal energy Of supercritical states.