  We build a new class of generative algorithms capable of efficiently learning
an arbitrary target distribution from possibly scarce, high-dimensional data
and subsequently generate new samples. These generative algorithms are
particle-based and are constructed as gradient flows of Lipschitz-regularized
Kullback-Leibler or other $f$-divergences, where data from a source
distribution can be stably transported as particles, towards the vicinity of
the target distribution. As a highlighted result in data integration, we
demonstrate that the proposed algorithms correctly transport gene expression
data points with dimension exceeding 54K, while the sample size is typically
only in the hundreds.
