We describe methods for the measurement of translational diffusion in very large static magnetic field gradients by NMR. The techniques use a "hole-burning" sequence that, with the use of fringe field gradients of 42 T/m, can image diffusion along one dimension on a submicron scale. Two varieties of this method are demonstrated, including a particularly efficient mode called the "hole-comb," in which multiple diffusion times comprising an entire diffusive evolution can be measured within the span of a single detected slice. The advantages and disadvantages of these methods are discussed, as well as their potential for addressing non-Fickian diffusion, diffusion in restricted media, and spatially inhomogeneous diffusion.