  We establish uniform bounds on the low-order derivatives of Stein equation
solutions for a broad class of multivariate, strongly log-concave target
distributions. These "Stein factor" bounds deliver control over Wasserstein and
related smooth function distances and are well-suited to analyzing the
computable Stein discrepancy measures of Gorham and Mackey. Our arguments of
proof are probabilistic and feature the synchronous coupling of multiple
overdamped Langevin diffusions.
