# Progressive Neural Image Compression with Nested Quantization and Latent Ordering

arXiv: https://arxiv.org/abs/2102.02913 · HTML: https://mlsanity.com/paper/2102.02913/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 4 Feb 2021.

## Builds on (most cited first, 13 of 13)

- [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)
- [DVC: An End-to-end Deep Video Compression Framework](https://mlsanity.com/paper/1812.00101/) (2018)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Video Compression With Rate-Distortion Autoencoders](https://mlsanity.com/paper/1908.05717/) (2019)
- [Learning Ordered Representations with Nested Dropout](https://mlsanity.com/paper/1402.0915/) (2014)
- [Feedback Recurrent Autoencoder for Video Compression](https://mlsanity.com/paper/2004.04342/) (2020)
- [Hierarchical Autoregressive Modeling for Neural Video Compression](https://mlsanity.com/paper/2010.10258/) (2020)
- [Variable Rate Image Compression Method with Dead-zone Quantizer](https://mlsanity.com/paper/2004.05855/) (2020)

## Built on by (most cited first, 24 of 24)

- [A Residual Diffusion Model for High Perceptual Quality Codec Augmentation](https://mlsanity.com/paper/2301.05489/) (2023)
- [Supervised Compression for Resource-Constrained Edge Computing Systems](https://mlsanity.com/paper/2108.11898/) (2021)
- [Extending Neural P-frame Codecs for B-frame Coding](https://mlsanity.com/paper/2104.00531/) (2021)
- [Context-Based Trit-Plane Coding for Progressive Image Compression](https://mlsanity.com/paper/2303.05715/) (2023)
- [MobileCodec: Neural Inter-frame Video Compression on Mobile Devices](https://mlsanity.com/paper/2207.08338/) (2022)
- [Selective compression learning of latent representations for variable-rate image compression](https://mlsanity.com/paper/2211.04104/) (2022)
- [Once-for-All: Controllable Generative Image Compression with Dynamic Granularity Adaptation](https://mlsanity.com/paper/2406.00758/) (2024)
- [SC2 Benchmark: Supervised Compression for Split Computing](https://mlsanity.com/paper/2203.08875/) (2022)
- [Progressive Compression with Universally Quantized Diffusion Models](https://mlsanity.com/paper/2412.10935/) (2024)
- [DeepHQ: Learned Hierarchical Quantizer for Progressive Deep Image Coding](https://mlsanity.com/paper/2408.12150/) (2024)
- [Efficient Progressive Image Compression with Variance-aware Masking](https://mlsanity.com/paper/2411.10185/) (2024)
- [COMPASS: High-Efficiency Deep Image Compression with Arbitrary-scale Spatial Scalability](https://mlsanity.com/paper/2309.07926/) (2023)
- [Progressive Neural Compression for Adaptive Image Offloading under Timing Constraints](https://mlsanity.com/paper/2310.05306/) (2023)
- [Region-of-Interest Based Neural Video Compression](https://mlsanity.com/paper/2203.01978/) (2022)
- [Learned Compression of Point Cloud Geometry and Attributes in a Single Model through Multimodal Rate-Control](https://mlsanity.com/paper/2408.00599/) (2024)
- [LimitNet: Progressive, Content-Aware Image Offloading for Extremely Weak Devices & Networks](https://mlsanity.com/paper/2504.13736/) (2025)
- [Neural Weight Compression for Language Models](https://mlsanity.com/paper/2510.11234/) (2025)
- [Progressive Learned Image Compression for Machine Perception](https://mlsanity.com/paper/2512.20070/) (2025)
- [Ordered and Binary Speaker Embedding](https://mlsanity.com/paper/2305.16043/) (2023)
- [FrameCorr: Adaptive, Autoencoder-based Neural Compression for Video Reconstruction in Resource and Timing Constrained Network Settings](https://mlsanity.com/paper/2409.02453/) (2024)
- [HCF: Hierarchical Cascade Framework for Distributed Multi-Stage Image Compression](https://mlsanity.com/paper/2508.02051/) (2025)
- [ProDAT: Progressive Density-Aware Tail-Drop for Point Cloud Coding](https://mlsanity.com/paper/2510.17068/) (2025)
- [Coarse-to-Fine: Progressive Image Compression for Semantically Hierarchical Classification](https://mlsanity.com/paper/2605.08266/) (2026)
- [Proteus: A Truncation-Robust Entropy Model for Progressive LiDAR Compression](https://mlsanity.com/paper/2608.00687/) (2026)

## Abstract (arXiv)

We present PLONQ, a progressive neural image compression scheme which pushes the boundary of variable bitrate compression by allowing quality scalable coding with a single bitstream. In contrast to existing learned variable bitrate solutions which produce separate bitstreams for each quality, it enables easier rate-control and requires less storage. Leveraging the latent scaling based variable bitrate solution, we introduce nested quantization, a method that defines multiple quantization levels with nested quantization grids, and progressively refines all latents from the coarsest to the finest quantization level. To achieve finer progressiveness in between any two quantization levels, latent elements are incrementally refined with an importance ordering defined in the rate-distortion sense. To the best of our knowledge, PLONQ is the first learning-based progressive image coding scheme and it outperforms SPIHT, a well-known wavelet-based progressive image codec.