  In models of freeze-in the dark matter (DM) is decoupled from the visible
sector and initially has a depleted number density. The hidden and visible
sectors are connected only via a feeble portal interaction by which DM can be
produced. Asymmetric freeze-in (AFI) combines this scenario with ideas from
asymmetric DM and provides a potential cogenesis mechanism. However, it has
been argued that existing AFI models do not produce suitably large particle
asymmetries due to cancellations which arises because the mediator state
remains in thermal equilibrium. We examine AFI via an out-of-equilibrium
mediator and using a simple scalar model show that in this case sizeable
asymmetries may be generated.
