Grand unified theories based on large groups (with rank greater or equal to 6 are a natural context for dark matter models. They contain Standard-Model-singlet fermions that could be dark matter candidates, and can contain new non-abelian interactions whose sphalerons convert baryons, leptons, and dark matter into each other, "cogenerating" a dark matter asymmetry comparable to the baryon asymmetry. In this paper it is shown that the same non-abelian interactions can "pre-annihilate" the symmetric component of heavy dark matter particles, which then decay late into light stable dark matter particles that inherit their asymmetry. It is shown that such decays can come from d=5 operators that are Planck or GUT suppressed. We derive constraints on such models and present a simple realization based on the group SU(7).

14 pages, a fully unified model presented in much greater detail