The modulated intensity by zero effort small-angle neutron scattering (MI-SANS) technique is used to measure scattering with a high energy resolution on samples normally ill-suited for neutron resonance spin echo. The self-diffusion constant of water is measured over a q-t range of 0.01-0.2Å-1 and 70-500ps. In addition to demonstrating the methodology of using time-of-flight MI-SANS instruments to observe diffusion in liquids, the results support previous measurements on water performed with different methods. This polarized neutron technique simultaneously measures the intermediate scattering function for a wide range of time and length scales. Two radio frequency flippers were used in a spin-echo setup with a 100kHz frequency difference in order to create a high-resolution time measurement. The results are compared with self-diffusion measurements made by other techniques and the general applicability of MI-SANS at a pulsed source is assessed.