The diffusion process in supercooled liquid water has been studied by a series of molecular dynamics simulations using systems of 216 ST2-model molecules in the temperature range between 255 and 360 K. In contrast to SPC/E water (Phys. Rev. E 1996, 54, 6331), the ST2 liquid does not show the appearance of a kinetic glass transition with structural arrest. Instead, we observe a significant change of the diffusion mechanism in the deeply supercooled region. The high-temperature microstep diffusion mechanism transforms continuously into a jump-diffusive behavior at low temperatures. By analyzing the intermediate incoherent structure factor of the center of mass motion we can characterize the hopping process by an average residence time tau(0). The hopping process is found to control reorientational and translational motions, leading to a second region of apparent Arrhenius behavior with a high activation energy of about 115 kJ mol(-1). The change in the dynamic behavior occurs in parallel to the structural and thermodynamical transformation to a low-density liquid form of ST2 water.