  Recent work has shown that Variational Autoencoders (VAEs) can be used to
upper-bound the information rate-distortion (R-D) function of images, i.e., the
fundamental limit of lossy image compression. In this paper, we report an
improved upper bound on the R-D function of images implemented by (1)
introducing a new VAE model architecture, (2) applying variable-rate
compression techniques, and (3) proposing a novel \ourfunction{} to stabilize
training. We demonstrate that at least 30\% BD-rate reduction w.r.t. the intra
prediction mode in VVC codec is achievable, suggesting that there is still
great potential for improving lossy image compression. Code is made publicly
available at https://github.com/duanzhiihao/lossy-vae.
