# Compressing Images by Encoding Their Latent Representations with Relative Entropy Coding

arXiv: https://arxiv.org/abs/2010.01185 · HTML: https://mlsanity.com/paper/2010.01185/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 30 of 39)

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- [Improving Lossless Compression Rates via Monte Carlo Bits-Back Coding](https://mlsanity.com/paper/2102.11086/) (2021)
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- [Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding](https://mlsanity.com/paper/2204.01612/) (2022)
- [RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations](https://mlsanity.com/paper/2309.17182/) (2023)
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- [Language-Enhanced Latent Representations for Out-of-Distribution Detection in Autonomous Driving](https://mlsanity.com/paper/2405.01691/) (2024)
- [Some Notes on the Sample Complexity of Approximate Channel Simulation](https://mlsanity.com/paper/2405.04363/) (2024)
- [Accelerating Relative Entropy Coding with Space Partitioning](https://mlsanity.com/paper/2405.12203/) (2024)
- [List-Level Distribution Coupling with Applications to Speculative Decoding and Lossy Compression](https://mlsanity.com/paper/2506.05632/) (2025)
- [ARC-AGI Without Pretraining](https://mlsanity.com/paper/2512.06104/) (2025)
- [On In-network learning. A Comparative Study with Federated and Split Learning](https://mlsanity.com/paper/2104.14929/) (2021)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
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## Abstract (arXiv)

Variational Autoencoders (VAEs) have seen widespread use in learned image compression. They are used to learn expressive latent representations on which downstream compression methods can operate with high efficiency. Recently proposed 'bits-back' methods can indirectly encode the latent representation of images with codelength close to the relative entropy between the latent posterior and the prior. However, due to the underlying algorithm, these methods can only be used for lossless compression, and they only achieve their nominal efficiency when compressing multiple images simultaneously; they are inefficient for compressing single images. As an alternative, we propose a novel method, Relative Entropy Coding (REC), that can directly encode the latent representation with codelength close to the relative entropy for single images, supported by our empirical results obtained on the Cifar10, ImageNet32 and Kodak datasets. Moreover, unlike previous bits-back methods, REC is immediately applicable to lossy compression, where it is competitive with the state-of-the-art on the Kodak dataset.