# ANFIC: Image Compression Using Augmented Normalizing Flows

arXiv: https://arxiv.org/abs/2107.08470 · HTML: https://mlsanity.com/paper/2107.08470/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 18 Jul 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [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)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [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)
- [Context-adaptive Entropy Model for End-to-end Optimized Image Compression](https://mlsanity.com/paper/1809.10452/) (2018)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Non-local Attention Optimized Deep Image Compression](https://mlsanity.com/paper/1904.09757/) (2019)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models](https://mlsanity.com/paper/2002.07101/) (2020)
- [Learning End-to-End Lossy Image Compression: A Benchmark](https://mlsanity.com/paper/2002.03711/) (2020)
- [Lossy Image Compression with Normalizing Flows](https://mlsanity.com/paper/2008.10486/) (2020)

## Built on by (most cited first, 20 of 20)

- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [CANF-VC: Conditional Augmented Normalizing Flows for Video Compression](https://mlsanity.com/paper/2207.05315/) (2022)
- [Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling](https://mlsanity.com/paper/2404.12940/) (2024)
- [B-CANF: Adaptive B-frame Coding with Conditional Augmented Normalizing Flows](https://mlsanity.com/paper/2209.01769/) (2022)
- [Hierarchical B-frame Video Coding Using Two-Layer CANF without Motion Coding](https://mlsanity.com/paper/2304.02690/) (2023)
- [High-Fidelity Variable-Rate Image Compression via Invertible Activation Transformation](https://mlsanity.com/paper/2209.05054/) (2022)
- [Learned Image Compression with Generalized Octave Convolution and Cross-Resolution Parameter Estimation](https://mlsanity.com/paper/2209.03353/) (2022)
- [Learned Scalable Video Coding For Humans and Machines](https://mlsanity.com/paper/2307.08978/) (2023)
- [Make Lossy Compression Meaningful for Low-Light Images](https://mlsanity.com/paper/2305.15030/) (2023)
- [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)
- [Survey on Visual Signal Coding and Processing with Generative Models: Technologies, Standards and Optimization](https://mlsanity.com/paper/2405.14221/) (2024)
- [Approximately Invertible Neural Network for Learned Image Compression](https://mlsanity.com/paper/2408.17073/) (2024)
- [Learned Video Compression for YUV 4:2:0 Content Using Flow-based Conditional Inter-frame Coding](https://mlsanity.com/paper/2210.08225/) (2022)
- [Content-Adaptive Motion Rate Adaption for Learned Video Compression](https://mlsanity.com/paper/2302.06293/) (2023)
- [NN-VVC: Versatile Video Coding boosted by self-supervisedly learned image coding for machines](https://mlsanity.com/paper/2401.10761/) (2024)
- [Transformations in Learned Image Compression from a Modulation Perspective](https://mlsanity.com/paper/2203.02158/) (2022)
- [Learned Hierarchical B-frame Coding with Adaptive Feature Modulation for YUV 4:2:0 Content](https://mlsanity.com/paper/2212.14187/) (2022)
- [Multiscale Augmented Normalizing Flows for Image Compression](https://mlsanity.com/paper/2305.05451/) (2023)
- [Learned Multimodal Compression for Autonomous Driving](https://mlsanity.com/paper/2408.08211/) (2024)
- [High-Fidelity Video Compression based on Invertible Neural Transform and Implicit Conditioning](https://mlsanity.com/paper/2606.13957/) (2026)

## Abstract (arXiv)

This paper introduces an end-to-end learned image compression system, termed ANFIC, based on Augmented Normalizing Flows (ANF). ANF is a new type of flow model, which stacks multiple variational autoencoders (VAE) for greater model expressiveness. The VAE-based image compression has gone mainstream, showing promising compression performance. Our work presents the first attempt to leverage VAE-based compression in a flow-based framework. ANFIC advances further compression efficiency by stacking and extending hierarchically multiple VAE's. The invertibility of ANF, together with our training strategies, enables ANFIC to support a wide range of quality levels without changing the encoding and decoding networks. Extensive experimental results show that in terms of PSNR-RGB, ANFIC performs comparably to or better than the state-of-the-art learned image compression. Moreover, it performs close to VVC intra coding, from low-rate compression up to nearly-lossless compression. In particular, ANFIC achieves the state-of-the-art performance, when extended with conditional convolution for variable rate compression with a single model.