Appendix A Analysis of variance of uncertainty estimators We demonstrate the lower variance of the Importance sampling-based estimator compared to the naive Monte

Carlo estimator, focusing on the Character V AE for molecular generation setting described in 5.3.1 and Importance sampling-based estimator (IS-MI) described in 3, and the naive Monte Carlo (MC-MI) equivalent. (Figure 1). The training dataset is comprised of 60k images and the test dataset is comprised of 10k images. No data augmentation is used at train time nor at inference. We jointly train a variational autoencoder with an auxiliary network (the "Property network") predicting digit thickness based on latent representation (see Figure 1).