Microscopic robots with features comparable with the wavelength of light offer new ways of probing the microscopic world and controlling light at the microscale. We introduce a new class of magnetically controlled microscopic robots (microbots) that operate at the visible-light diffraction limit, which we term diffractive robots. We combined nanometer-thick mechanical membranes, programmable nanomagnets, and diffractive optical elements to create untethered microbots small enough to diffract visible light and flexible enough to undergo complex reconfigurations in millitesla-scale magnetic fields. We demonstrated their applications, 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.