# NVTC: Nonlinear Vector Transform Coding

arXiv: https://arxiv.org/abs/2305.16025 · HTML: https://mlsanity.com/paper/2305.16025/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Improving Inference for Neural Image Compression](https://mlsanity.com/paper/2006.04240/) (2020)
- [Causal Contextual Prediction for Learned Image Compression](https://mlsanity.com/paper/2011.09704/) (2020)
- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [Unified Multivariate Gaussian Mixture for Efficient Neural Image Compression](https://mlsanity.com/paper/2203.10897/) (2022)

## Built on by (most cited first, 14 of 14)

- [MLIC++: Linear Complexity Multi-Reference Entropy Modeling for Learned Image Compression](https://mlsanity.com/paper/2307.15421/) (2023)
- [Approaching Rate-Distortion Limits in Neural Compression with Lattice Transform Coding](https://mlsanity.com/paper/2403.07320/) (2024)
- [Learning Optimal Lattice Vector Quantizers for End-to-end Neural Image Compression](https://mlsanity.com/paper/2411.16119/) (2024)
- [Balanced Rate-Distortion Optimization in Learned Image Compression](https://mlsanity.com/paper/2502.20161/) (2025)
- [ProGIC: Progressive and Lightweight Generative Image Compression with Residual Vector Quantization](https://mlsanity.com/paper/2603.02897/) (2026)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
- [Why Compress What You Can Generate? When GPT-4o Generation Ushers in Image Compression Fields](https://mlsanity.com/paper/2504.21814/) (2025)
- [Leveraging Second-Order Curvature for Efficient Learned Image Compression: Theory and Empirical Evidence](https://mlsanity.com/paper/2601.20769/) (2026)
- [An Information-Theoretic Regularizer for Lossy Neural Image Compression](https://mlsanity.com/paper/2411.16727/) (2024)
- [Exploiting Latent Properties to Optimize Neural Codecs](https://mlsanity.com/paper/2501.01231/) (2025)
- [Comp-X: On Defining an Interactive Learned Image Compression Paradigm With Expert-driven LLM Agent](https://mlsanity.com/paper/2508.15243/) (2025)
- [HyperVQ: Enabling Hyperprior Entropy Modeling for VQ-Based Generative Image Compression](https://mlsanity.com/paper/2512.07192/) (2025)
- [Control Your View: High-Resolution Global Semantic Manipulation in Learned Image Compression](https://mlsanity.com/paper/2605.08727/) (2026)
- [Tree-VQ: Progressive Image Compression from Pretrained Vector Quantizers](https://mlsanity.com/paper/2609.03641/) (2026)

## Abstract (arXiv)

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