We demonstrate that a position correlation magnetic resonance imaging (MRI) experiment based on two phase encoding steps separated by a delay can be used for quantifying diffusion across a membrane. This method is noninvasive, and no tracer substance or concentration gradient across the membrane is required. Because, in typical membranes, the T-1 relaxation time of the fluid spins is usually much longer than the T-2 time, we developed and implemented a new position correlation experiment based on a stimulated spin-echo, in which the relaxation attenuation of the signal is dominated by T-1 instead of T-2. This enables using relatively long delays needed in the diffusion measurements. The sensitivity of the double encoded experiment detected in a conventional way is still low because of the low filling factor of the fluid inside the NMR coil around the sample. We circumvent this problem by using the remote detection technique, which significantly increases the sensitivity, making it possible to do the measurements with gaseous fluids that have a low spin-density compared to liquids. We derive a model that enables us to extract a diffusion constant characterizing the diffusion rate through the membrane from the obtained correlation images. The double phase encoded MRI method is advantageous in any kind of diffusion studies, because the propagator of fluid molecules can directly be seen from the correlation image.