  In this note, we establish a descent lemma for the population limit Mirrored
Stein Variational Gradient Method~(MSVGD). This descent lemma does not rely on
the path information of MSVGD but rather on a simple assumption for the
mirrored distribution $\nabla\Psi_{\#}\pi\propto\exp(-V)$. Our analysis
demonstrates that MSVGD can be applied to a broader class of constrained
sampling problems with non-smooth $V$. We also investigate the complexity of
the population limit MSVGD in terms of dimension $d$.
