Abstract: Many models of dark matter contain more than one new particle beyond those in the Standard Model. Often, heavier particles decay into the lightest dark matter particle as the Universe evolves. Here, we explore the possibilities which arise if one of the products in a (heavy particle) -> (dark matter) decay is a positron, and the lifetime is shorter than the age of the Universe. The positrons cool down by scattering off the cosmic microwave background and eventually annihilate when they fall into Galactic potential wells. The resulting 511 keV flux not only places constraints on this class of models, but might even be consistent with that observed by the INTEGRAL satellite.