  This paper addresses the problem of lossy image compression, a fundamental
problem in image processing and information theory that is involved in many
real-world applications. We start by reviewing the framework of variational
autoencoders (VAEs), a powerful class of generative probabilistic models that
has a deep connection to lossy compression. Based on VAEs, we develop a novel
scheme for lossy image compression, which we name quantization-aware ResNet VAE
(QARV). Our method incorporates a hierarchical VAE architecture integrated with
test-time quantization and quantization-aware training, without which efficient
entropy coding would not be possible. In addition, we design the neural network
architecture of QARV specifically for fast decoding and propose an adaptive
normalization operation for variable-rate compression. Extensive experiments
are conducted, and results show that QARV achieves variable-rate compression,
high-speed decoding, and a better rate-distortion performance than existing
baseline methods. The code of our method is publicly accessible at
https://github.com/duanzhiihao/lossy-vae
