Reviews: Stein Variational Gradient Descent as Gradient Flow

The paper provides asymptotic convergence results, both in the large-particle and large-time limits. The paper also investigates the continuous-time limit of SVGD, which results in a PDE that has the flavor of a deterministic Fokker-Planck equation. Finally, the paper offers a geometric perspective, interpreting the continuous-time process as a gradient flow and introducing a novel optimal transport metric along the way. Overall, this is a very nice paper with some insightful results. However, there are a few important technical issues that prevent me from recommending publication.