We propose a novel mechanism for the production of dark matter (DM) from a thermal bath based on the idea that DM particles χ can transform heat bath particles ψ : χ ψ →χ χ . For a small initial abundance of χ , this leads to an exponential growth of the DM number density in close analogy to other familiar exponential growth processes in nature. We demonstrate that this mechanism complements freeze-in and freeze-out production in a generic way, opening new parameter space to explain the observed DM abundance, and we discuss observational prospects for such scenarios.