  We study a mechanism through which the cosmic dark matter density can be
explained simultaneously with the observed baryon asymmetry of the Universe. At
the core of our proposal lie the out-of-equilibrium scattering processes of
bath particles which are responsible for the production of feebly-interacting
dark matter. The same processes violate $CP$, which further leads to an
asymmetry between matter and antimatter being generated in the visible sector.
We focus on the possibility that these interactions are described through
non-renormalizable operators, which leads to both dark matter and the baryon
asymmetry being produced at high temperatures. The mechanism is exemplified by
studying two concrete scenarios, one involving scalar and one involving fermion
dark matter. We find that in both cases it is, indeed, possible to achieve a
common explanation for the dark matter content and the matter-antimatter
asymmetry of the Universe, provided that dark matter is in the keV mass range.
