  Quantization is one of the core components in lossy image compression. For
neural image compression, end-to-end optimization requires differentiable
approximations of quantization, which can generally be grouped into three
categories: additive uniform noise, straight-through estimator and soft-to-hard
annealing. Training with additive uniform noise approximates the quantization
error variationally but suffers from the train-test mismatch. The other two
methods do not encounter this mismatch but, as shown in this paper, hurt the
rate-distortion performance since the latent representation ability is
weakened. We thus propose a novel soft-then-hard quantization strategy for
neural image compression that first learns an expressive latent space softly,
then closes the train-test mismatch with hard quantization. In addition, beyond
the fixed integer quantization, we apply scaled additive uniform noise to
adaptively control the quantization granularity by deriving a new variational
upper bound on actual rate. Experiments demonstrate that our proposed methods
are easy to adopt, stable to train, and highly effective especially on complex
compression models.
