Microscopic robots with features comparable with the wavelength of light offer new ways of probing the microscopic world and controlling light at the microscale. Here, a new class of magnetically controlled microscopic robots (microbots) are introduced that operate at the visible-light diffraction limit, which were termed diffractive robots. Nanometer-thick mechanical membranes, programmable nanomagnets, and diffractive optical elements were combined to create untethered microbots small enough to diffract visible light and flexible enough to undergo complex reconfigurations in millitesla-scale magnetic fields. Their applications were demonstrated, including subdiffractive imaging by using a variant of structured illumination microscopy, tunable diffractive optical elements for beam steering and focusing, and force sensing with piconewton sensitivity.