# Split Hierarchical Variational Compression

arXiv: https://arxiv.org/abs/2204.02071 · HTML: https://mlsanity.com/paper/2204.02071/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 30 of 32)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Channel-wise Autoregressive Entropy Models for Learned Image Compression](https://mlsanity.com/paper/2007.08739/) (2020)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [SalsaNext: Fast, Uncertainty-aware Semantic Segmentation of LiDAR Point Clouds for Autonomous Driving](https://mlsanity.com/paper/2003.03653/) (2020)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Practical Full Resolution Learned Lossless Image Compression](https://mlsanity.com/paper/1811.12817/) (2018)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Practical Lossless Compression with Latent Variables using Bits Back Coding](https://mlsanity.com/paper/1901.04866/) (2019)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Parallel Multiscale Autoregressive Density Estimation](https://mlsanity.com/paper/1703.03664/) (2017)
- [PixelVAE: A Latent Variable Model for Natural Images](https://mlsanity.com/paper/1611.05013/) (2016)
- [ELF-VC: Efficient Learned Flexible-Rate Video Coding](https://mlsanity.com/paper/2104.14335/) (2021)
- [Bit-Swap: Recursive Bits-Back Coding for Lossless Compression with Hierarchical Latent Variables](https://mlsanity.com/paper/1905.06845/) (2019)
- [HiLLoC: Lossless Image Compression with Hierarchical Latent Variable Models](https://mlsanity.com/paper/1912.09953/) (2019)
- [IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression](https://mlsanity.com/paper/2006.12459/) (2020)
- [Compression with Flows via Local Bits-Back Coding](https://mlsanity.com/paper/1905.08500/) (2019)
- [Learning Better Lossless Compression Using Lossy Compression](https://mlsanity.com/paper/2003.10184/) (2020)
- [iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compression](https://mlsanity.com/paper/2103.16211/) (2021)
- [iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Coder](https://mlsanity.com/paper/2111.00965/) (2021)
- [Lossless Image Compression through Super-Resolution](https://mlsanity.com/paper/2004.02872/) (2020)

## Built on by (most cited first, 5 of 5)

- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [QARV: Quantization-Aware ResNet VAE for Lossy Image Compression](https://mlsanity.com/paper/2302.08899/) (2023)
- [Multi-Sample Training for Neural Image Compression](https://mlsanity.com/paper/2209.13834/) (2022)
- [LVPNet: A Latent-variable-based Prediction-driven End-to-end Framework for Lossless Compression of Medical Images](https://mlsanity.com/paper/2506.17983/) (2025)
- [Proteus: A Truncation-Robust Entropy Model for Progressive LiDAR Compression](https://mlsanity.com/paper/2608.00687/) (2026)

## Abstract (arXiv)

Variational autoencoders (VAEs) have witnessed great success in performing the compression of image datasets. This success, made possible by the bits-back coding framework, has produced competitive compression performance across many benchmarks. However, despite this, VAE architectures are currently limited by a combination of coding practicalities and compression ratios. That is, not only do state-of-the-art methods, such as normalizing flows, often demonstrate out-performance, but the initial bits required in coding makes single and parallel image compression challenging. To remedy this, we introduce Split Hierarchical Variational Compression (SHVC). SHVC introduces two novelties. Firstly, we propose an efficient autoregressive prior, the autoregressive sub-pixel convolution, that allows a generalisation between per-pixel autoregressions and fully factorised probability models. Secondly, we define our coding framework, the autoregressive initial bits, that flexibly supports parallel coding and avoids -- for the first time -- many of the practicalities commonly associated with bits-back coding. In our experiments, we demonstrate SHVC is able to achieve state-of-the-art compression performance across full-resolution lossless image compression tasks, with up to 100x fewer model parameters than competing VAE approaches.