Genetic variation increases during biological invasion by a Cuban lizard (Nature):

A genetic paradox exists in invasion biology: how do introduced populations, whose genetic variation has probably been depleted by population bottlenecks, persist and adapt to new conditions...Genetic analyses indicate that at least eight introductions have occurred in Florida from across this lizard's native range, blending genetic variation from different geographic source populations and producing populations that contain substantially more, not less, genetic variation than native populations. Moreover, recently introduced brown anole populations around the world originate from Florida, and some have maintained these elevated levels of genetic variation. Here we show that one key to invasion success may be the occurrence of multiple introductions that transform among-population variation in native ranges to within-population variation in introduced areas.

Basically, you have a process where various demes have fixed (or moved toward that direction) on various loci. The initially low level of polymorphism is further depleted by the enormous sampling error that often occurs during selection for a founding event. But, these originally isolated genetic populations came into contact and mixed, producing genetically varied descendent populations.

The moral is that there are many ways that nature reduces genetic diversity, from random genetic drift to persistent directional selection, but migration is one way that intrapopulational diversity can increase.

Full paper (PDF).

Addendum: change in allelic frequency = proportion of migrants in parental generation of given population * (frequency of allele in parental population of given population for non-migrants - frequency of allele in parental population of given population for migrants), or change Δp = m * (p_{natives at t} - p_{migrants at t}).

Related: Fisher's "Fundamental Theorem of Natural Selection": The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time. In short, the rate of evolutionary change is proportional to the genotypic variation that selection has to work with. Here is the related math.