The influence rapid solidification under local nonequilibrium solute diffusion on a solute concentration field, solute partitioning, interface temperature, and absolute stability limit is studied. The analysis shows a transition from diffusion-controlled solidification to purely thermal controlled regimes, which occurs abruptly when the interface velocity equals the bulk liquid diffusive speed. The abrupt change in the solidification is described by the velocity-dependent effective diffusion coefficient and the generalized partition coefficient.