  Isocurvature fluctuations, where the relative number density of particle
species spatially varies, can be generated from initially adiabatic, or
curvature, fluctuations if the various species fall out of or were never in
thermal equilibrium. The freezing of the thermal relic dark matter abundance is
one such case, but for modes that are still outside the horizon the amplitude
is highly suppressed and originates from the small change in the local
expansion rate due to the local space curvature produced by the curvature
fluctuation. We establish a simple separate-universe method for calculating
this generation that applies to both freeze-in and freeze-out models, identify
three critical epochs for this process, and give general scaling behaviors for
the amplitude in each case: the freezing epoch, the kinetic decoupling epoch
and matter-radiation equality. Freeze-out models are typically dominated by
spatially modulated annihilation from the latter epochs and can generate much
larger isocurvature fluctuations compared with typical freeze-in models, albeit
still very small and observationally allowed by cosmic microwave background
measurements. We illustrate these results with concrete models where the dark
matter interactions are vector or scalar mediated.
