Appendix for: Invertible Gaussian Reparameterization

As mentioned in section 3.1, we can use the matrix determinant lemma to efficiently compute the determinant of the Jacobian of the softmax Proof: For k = 1,..., K 1, we have: P(H = k) = Note that the involved integrals are one-dimensional and thus can be accurately approximated with quadrature methods. As mentioned in the main manuscript, our VAE experiments closely follow Maddison et al. [4]: we use the same continuous objective and the same evaluation metrics. Using the former KL results in optimizing a continuous objective which is not a log-likelihood lower bound anymore, which is mainly why we followed Maddison et al. [4]. In addition to the reported comparisons in the main manuscript, we include further comparisons in Table 1 reporting the discretized training ELBO instead. These are variance reduction techniques which heavily lean on the GS to improve the variance of the obtained gradients.