# iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Coder

arXiv: https://arxiv.org/abs/2111.00965 · HTML: https://mlsanity.com/paper/2111.00965/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 25 of 25)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Practical Full Resolution Learned Lossless Image Compression](https://mlsanity.com/paper/1811.12817/) (2018)
- [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)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Bit-Swap: Recursive Bits-Back Coding for Lossless Compression with Hierarchical Latent Variables](https://mlsanity.com/paper/1905.06845/) (2019)
- [VFlow: More Expressive Generative Flows with Variational Data Augmentation](https://mlsanity.com/paper/2002.09741/) (2020)
- [HiLLoC: Lossless Image Compression with Hierarchical Latent Variable Models](https://mlsanity.com/paper/1912.09953/) (2019)
- [Categorical Normalizing Flows via Continuous Transformations](https://mlsanity.com/paper/2006.09790/) (2020)
- [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)
- [Lossless Image Compression through Super-Resolution](https://mlsanity.com/paper/2004.02872/) (2020)
- [Learning Discrete Distributions by Dequantization](https://mlsanity.com/paper/2001.11235/) (2020)

## Built on by (most cited first, 26 of 26)

- [QARV: Quantization-Aware ResNet VAE for Lossy Image Compression](https://mlsanity.com/paper/2302.08899/) (2023)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Large Language Model for Lossless Image Compression with Visual Prompts](https://mlsanity.com/paper/2502.16163/) (2025)
- [Large Language Models for Lossless Image Compression: Next-Pixel Prediction in Language Space is All You Need](https://mlsanity.com/paper/2411.12448/) (2024)
- [GroupedMixer: An Entropy Model with Group-wise Token-Mixers for Learned Image Compression](https://mlsanity.com/paper/2405.01170/) (2024)
- [CALLIC: Content Adaptive Learning for Lossless Image Compression](https://mlsanity.com/paper/2412.17464/) (2024)
- [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)
- [Learning Lossless Compression for High Bit-Depth Volumetric Medical Image](https://mlsanity.com/paper/2410.17814/) (2024)
- [Parallel Neural Local Lossless Compression](https://mlsanity.com/paper/2201.05213/) (2022)
- [Fast Lossless Neural Compression with Integer-Only Discrete Flows](https://mlsanity.com/paper/2206.08869/) (2022)
- [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)
- [Learned HDR Image Compression for Perceptually Optimal Storage and Display](https://mlsanity.com/paper/2407.13179/) (2024)
- [DualComp: End-to-End Learning of a Unified Dual-Modality Lossless Compressor](https://mlsanity.com/paper/2505.16256/) (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)
- [OmniZip: Learning a Unified and Lightweight Lossless Compressor for Multi-Modal Data](https://mlsanity.com/paper/2602.22286/) (2026)
- [Molecular Generative Adversarial Network with Multi-Property Optimization](https://mlsanity.com/paper/2404.00081/) (2024)
- [SEEC: Segmentation-Assisted Multi-Entropy Models for Learned Lossless Image Compression](https://mlsanity.com/paper/2509.07704/) (2025)
- [Multi-Scale Architectures Matter: On the Adversarial Robustness of Flow-based Lossless Compression](https://mlsanity.com/paper/2208.12716/) (2022)
- [The State of Applying Artificial Intelligence to Tissue Imaging for Cancer Research and Early Detection](https://mlsanity.com/paper/2306.16989/) (2023)
- [Edge Storage Management Recipe with Zero-Shot Data Compression for Road Anomaly Detection](https://mlsanity.com/paper/2307.04298/) (2023)
- [FLLIC: Functionally Lossless Image Compression](https://mlsanity.com/paper/2401.13616/) (2024)
- [Deep Robust Reversible Watermarking](https://mlsanity.com/paper/2503.02490/) (2025)
- [RAWIC: Bit-Depth Adaptive Lossless Raw Image Compression](https://mlsanity.com/paper/2603.28105/) (2026)
- [LUMI: Tokenizer-Agnostic LLM-Based Lossless Image Compression](https://mlsanity.com/paper/2607.08221/) (2026)
- [Practical Lossless Volumetric Medical Image Compression via Tri-plane Context Tree Learning](https://mlsanity.com/paper/2608.13897/) (2026)

## Abstract (arXiv)

It was estimated that the world produced 59 ZB (5.9 × 1013 GB) of data in 2020, resulting in the enormous costs of both data storage and transmission. Fortunately, recent advances in deep generative models have spearheaded a new class of so-called "neural compression" algorithms, which significantly outperform traditional codecs in terms of compression ratio. Unfortunately, the application of neural compression garners little commercial interest due to its limited bandwidth; therefore, developing highly efficient frameworks is of critical practical importance. In this paper, we discuss lossless compression using normalizing flows which have demonstrated a great capacity for achieving high compression ratios. As such, we introduce iFlow, a new method for achieving efficient lossless compression. We first propose Modular Scale Transform (MST) and a novel family of numerically invertible flow transformations based on MST. Then we introduce the Uniform Base Conversion System (UBCS), a fast uniform-distribution codec incorporated into iFlow, enabling efficient compression. iFlow achieves state-of-the-art compression ratios and is 5× quicker than other high-performance schemes. Furthermore, the techniques presented in this paper can be used to accelerate coding time for a broad class of flow-based algorithms.