1. A method for producing a diffusion weighted image with an MRI system, the steps comprising: a) performing a diffusion weighting pulse sequence in which transverse magnetization is produced by an rf excitation pulse, and the transverse magnetization is diffusion weighted by application of a bipolar gradient pulse; b) dephasing the diffusion weighted transverse magnetization by application of a first gradient pulse; c) saving a component of the diffusion weighted transverse magnetization by applying an rf pulse which tips the component into the longitudinal axis; d) dephasing transverse magnetization by applying a second gradient pulse; e) performing a fast spin echo pulse sequence in which the saved diffusion weighted magnetization is tipped into the transverse plane by an rf excitation pulse, and a series of NMR echo signals are produced by a corresponding series of rf refocusing pulses; and f) reconstructing an image from the acquired NMR echo signals.