Sampling from a target measure when only partial information is available (e.g. unnormalized density as in Bayesian inference, or true samples as in generative modeling) is a fundamental problem in computational statistics and machine learning. The sampling problem can be cast as an optimization one over the space of probability distributions of a well-chosen discrepancy,  e.g. a divergence or distance to the target. In this talk, I will discuss several properties of sampling algorithms for some choices of novel discrepancies based on reproducing kernels, both regarding their optimization and quantization aspects.