  In theory, vector quantization (VQ) is always better than scalar quantization
(SQ) in terms of rate-distortion (R-D) performance. Recent state-of-the-art
methods for neural image compression are mainly based on nonlinear transform
coding (NTC) with uniform scalar quantization, overlooking the benefits of VQ
due to its exponentially increased complexity. In this paper, we first
investigate on some toy sources, demonstrating that even if modern neural
networks considerably enhance the compression performance of SQ with nonlinear
transform, there is still an insurmountable chasm between SQ and VQ. Therefore,
revolving around VQ, we propose a novel framework for neural image compression
named Nonlinear Vector Transform Coding (NVTC). NVTC solves the critical
complexity issue of VQ through (1) a multi-stage quantization strategy and (2)
nonlinear vector transforms. In addition, we apply entropy-constrained VQ in
latent space to adaptively determine the quantization boundaries for joint
rate-distortion optimization, which improves the performance both theoretically
and experimentally. Compared to previous NTC approaches, NVTC demonstrates
superior rate-distortion performance, faster decoding speed, and smaller model
size. Our code is available at https://github.com/USTC-IMCL/NVTC
