# Compression with Flows via Local Bits-Back Coding

arXiv: https://arxiv.org/abs/1905.08500 · HTML: https://mlsanity.com/paper/1905.08500/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2019.

## Built on by (most cited first, 30 of 34)

- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [On the Out-of-distribution Generalization of Probabilistic Image Modelling](https://mlsanity.com/paper/2109.02639/) (2021)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [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)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Lossless Compression with Probabilistic Circuits](https://mlsanity.com/paper/2111.11632/) (2021)
- [Towards Empirical Sandwich Bounds on the Rate-Distortion Function](https://mlsanity.com/paper/2111.12166/) (2021)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [Insights from Generative Modeling for Neural Video Compression](https://mlsanity.com/paper/2107.13136/) (2021)
- [CALLIC: Content Adaptive Learning for Lossless Image Compression](https://mlsanity.com/paper/2412.17464/) (2024)
- [Lossless Image Compression Using a Multi-Scale Progressive Statistical Model](https://mlsanity.com/paper/2108.10551/) (2021)
- [Split Hierarchical Variational Compression](https://mlsanity.com/paper/2204.02071/) (2022)
- [PILC: Practical Image Lossless Compression with an End-to-end GPU Oriented Neural Framework](https://mlsanity.com/paper/2206.05279/) (2022)
- [Understanding Likelihood of Normalizing Flow and Image Complexity through the Lens of Out-of-Distribution Detection](https://mlsanity.com/paper/2402.10477/) (2024)
- [Lossless Compression with Latent Variable Models](https://mlsanity.com/paper/2104.10544/) (2021)
- [Fast Lossless Neural Compression with Integer-Only Discrete Flows](https://mlsanity.com/paper/2206.08869/) (2022)
- [Learning Non-linear Wavelet Transformation via Normalizing Flow](https://mlsanity.com/paper/2101.11306/) (2021)
- [Test-time adaptation for image compression with distribution regularization](https://mlsanity.com/paper/2410.12191/) (2024)
- [Discrete Denoising Flows](https://mlsanity.com/paper/2107.11625/) (2021)
- [Wavelet-Like Transform-Based Technology in Response to the Call for Proposals on Neural Network-Based Image Coding](https://mlsanity.com/paper/2403.05937/) (2024)
- [Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Maps](https://mlsanity.com/paper/2501.06999/) (2025)
- [LVPNet: A Latent-variable-based Prediction-driven End-to-end Framework for Lossless Compression of Medical Images](https://mlsanity.com/paper/2506.17983/) (2025)
- [Extreme-scale Talking-Face Video Upsampling with Audio-Visual Priors](https://mlsanity.com/paper/2208.08118/) (2022)
- [SEEC: Segmentation-Assisted Multi-Entropy Models for Learned Lossless Image Compression](https://mlsanity.com/paper/2509.07704/) (2025)
- [OSOA: One-Shot Online Adaptation of Deep Generative Models for Lossless Compression](https://mlsanity.com/paper/2111.01662/) (2021)

## Abstract (arXiv)

Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient codes that achieve these lengths, and coding algorithms must be hand-tailored to specific types of generative models to ensure computational efficiency. Such coding algorithms are known for autoregressive models and variational autoencoders, but not for general types of flow models. To fill in this gap, we introduce local bits-back coding, a new compression technique for flow models. We present efficient algorithms that instantiate our technique for many popular types of flows, and we demonstrate that our algorithms closely achieve theoretical codelengths for state-of-the-art flow models on high-dimensional data.