A methodology for chemical shift resolved molecular self-diffusion measurements in time-independent static and radiofrequency field gradients is demonstrated. Diffusion encoding is provided by a stimulated echo sequence with additional z-storage that allows for a change of diffusion time without affecting the relaxation weighting. The signal is acquired stroboscopically between the pulses of a train of adiabatic double passages that induces a z-rotation counteracting the phase spread resulting from precession in the inhomogeneous static field, as demonstrated in recent approaches to the goal of high-resolution "ex situ" NMR. Simulations of the pulse sequence show that the acquired signal results from the desired coherence pathway. Successful demonstrations of the experiment were performed on a mixture of water and isopropanol.