  Modeling latent variables with priors and hyperpriors is an essential problem
in variational image compression. Formally, trade-off between rate and
distortion is handled well if priors and hyperpriors precisely describe latent
variables. Current practices only adopt univariate priors and process each
variable individually. However, we find inter-correlations and
intra-correlations exist when observing latent variables in a vectorized
perspective. These findings reveal visual redundancies to improve
rate-distortion performance and parallel processing ability to speed up
compression. This encourages us to propose a novel vectorized prior.
Specifically, a multivariate Gaussian mixture is proposed with means and
covariances to be estimated. Then, a novel probabilistic vector quantization is
utilized to effectively approximate means, and remaining covariances are
further induced to a unified mixture and solved by cascaded estimation without
context models involved. Furthermore, codebooks involved in quantization are
extended to multi-codebooks for complexity reduction, which formulates an
efficient compression procedure. Extensive experiments on benchmark datasets
against state-of-the-art indicate our model has better rate-distortion
performance and an impressive $3.18\times$ compression speed up, giving us the
ability to perform real-time, high-quality variational image compression in
practice. Our source code is publicly available at
\url{https://github.com/xiaosu-zhu/McQuic}.
