The self-diffusion coefficient of water has been measured by the steady-gradient spin-echo method at pressures up to 2380 bar and temperatures between 2 and −20°C in the stable liquid range using both strengthened glass and beryllium–copper pressure vessels. At low temperatures and high pressures the diffusion coefficient becomes almost independent of pressure. However, a rapid increase in DH2O with the first kilobar of applied pressure is inferred for the supercooled liquid from the relation of the new data to the 1 atm pressure diffusivity of supercooled water. The observations may be correlated with the high pressure low temperature thermodynamic properties of water in a manner consistent with the Adam–Gibbs entropy theory of liquid transport processes.