The paper provides a clear presentation of variance bounds for reparameterization gradients for location scale families. The drawback is the limited applicability of the approach. In a revision, the paper should address the following concerns: - A more detailed discussion of the role of the entropy term - A paragraph on smoothness constants - A discussion on if the proof techniques would generalize to more general classes of variational approximation. If they don't, detailing the technical hurdle that limits this line of analysis would be worthwhile