  Among dissimilarities between probability distributions, the Kernel Stein
Discrepancy (KSD) has received much interest recently. We investigate the
properties of its Wasserstein gradient flow to approximate a target probability
distribution $\pi$ on $\mathbb{R}^d$, known up to a normalization constant.
This leads to a straightforwardly implementable, deterministic score-based
method to sample from $\pi$, named KSD Descent, which uses a set of particles
to approximate $\pi$. Remarkably, owing to a tractable loss function, KSD
Descent can leverage robust parameter-free optimization schemes such as L-BFGS;
this contrasts with other popular particle-based schemes such as the Stein
Variational Gradient Descent algorithm. We study the convergence properties of
KSD Descent and demonstrate its practical relevance. However, we also highlight
failure cases by showing that the algorithm can get stuck in spurious local
minima.
