# Joint Autoregressive and Hierarchical Priors for Learned Image Compression

arXiv: https://arxiv.org/abs/1809.02736 · HTML: https://mlsanity.com/paper/1809.02736/

## Key facts

- Cited by 664 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2018.

## Built on by (most cited first, 30 of 664)

- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Deep Contextual Video Compression](https://mlsanity.com/paper/2109.15047/) (2021)
- [Learned Image Compression with Mixed Transformer-CNN Architectures](https://mlsanity.com/paper/2303.14978/) (2023)
- [Checkerboard Context Model for Efficient Learned Image Compression](https://mlsanity.com/paper/2103.15306/) (2021)
- [Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications](https://mlsanity.com/paper/2207.09353/) (2022)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Neural Video Compression with Diverse Contexts](https://mlsanity.com/paper/2302.14402/) (2023)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [FVC: A New Framework towards Deep Video Compression in Feature Space](https://mlsanity.com/paper/2105.09600/) (2021)
- [The Devil Is in the Details: Window-based Attention for Image Compression](https://mlsanity.com/paper/2203.08450/) (2022)
- [Hybrid Spatial-Temporal Entropy Modelling for Neural Video Compression](https://mlsanity.com/paper/2207.05894/) (2022)
- [Temporal Context Mining for Learned Video Compression](https://mlsanity.com/paper/2111.13850/) (2021)
- [Entroformer: A Transformer-based Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2202.05492/) (2022)
- [Enhanced Invertible Encoding for Learned Image Compression](https://mlsanity.com/paper/2108.03690/) (2021)
- [Towards image compression with perfect realism at ultra-low bitrates](https://mlsanity.com/paper/2310.10325/) (2023)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Improving Statistical Fidelity for Neural Image Compression with Implicit Local Likelihood Models](https://mlsanity.com/paper/2301.11189/) (2023)
- [MLIC: Multi-Reference Entropy Model for Learned Image Compression](https://mlsanity.com/paper/2211.07273/) (2022)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [CompGS: Efficient 3D Scene Representation via Compressed Gaussian Splatting](https://mlsanity.com/paper/2404.09458/) (2024)
- [Multi-Realism Image Compression with a Conditional Generator](https://mlsanity.com/paper/2212.13824/) (2022)
- [Improving the Diffusability of Autoencoders](https://mlsanity.com/paper/2502.14831/) (2025)
- [Towards Practical Real-Time Neural Video Compression](https://mlsanity.com/paper/2502.20762/) (2025)
- [An Introduction to Neural Data Compression](https://mlsanity.com/paper/2202.06533/) (2022)
- [Nonlinear Transform Source-Channel Coding for Semantic Communications](https://mlsanity.com/paper/2112.10961/) (2021)
- [VCT: A Video Compression Transformer](https://mlsanity.com/paper/2206.07307/) (2022)
- [Sparse Tensor-based Multiscale Representation for Point Cloud Geometry Compression](https://mlsanity.com/paper/2111.10633/) (2021)
- [Transformer-based Image Compression](https://mlsanity.com/paper/2111.06707/) (2021)

## Abstract (arXiv)

Recent models for learned image compression are based on autoencoders, learning approximately invertible mappings from pixels to a quantized latent representation. These are combined with an entropy model, a prior on the latent representation that can be used with standard arithmetic coding algorithms to yield a compressed bitstream. Recently, hierarchical entropy models have been introduced as a way to exploit more structure in the latents than simple fully factorized priors, improving compression performance while maintaining end-to-end optimization. Inspired by the success of autoregressive priors in probabilistic generative models, we examine autoregressive, hierarchical, as well as combined priors as alternatives, weighing their costs and benefits in the context of image compression. While it is well known that autoregressive models come with a significant computational penalty, we find that in terms of compression performance, autoregressive and hierarchical priors are complementary and, together, exploit the probabilistic structure in the latents better than all previous learned models. The combined model yields state-of-the-art rate--distortion performance, providing a 15.8% average reduction in file size over the previous state-of-the-art method based on deep learning, which corresponds to a 59.8% size reduction over JPEG, more than 35% reduction compared to WebP and JPEG2000, and bitstreams 8.4% smaller than BPG, the current state-of-the-art image codec. To the best of our knowledge, our model is the first learning-based method to outperform BPG on both PSNR and MS-SSIM distortion metrics.