# Pixel Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1601.06759 · HTML: https://mlsanity.com/paper/1601.06759/

## Key facts

- Cited by 816 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2016.

## Built on by (most cited first, 30 of 816)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [VideoGPT: Video Generation using VQ-VAE and Transformers](https://mlsanity.com/paper/2104.10157/) (2021)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Aligning Text-to-Image Models using Human Feedback](https://mlsanity.com/paper/2302.12192/) (2023)
- [Instant3D: Fast Text-to-3D with Sparse-View Generation and Large Reconstruction Model](https://mlsanity.com/paper/2311.06214/) (2023)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)

## Abstract (arXiv)

Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts the pixels in an image along the two spatial dimensions. Our method models the discrete probability of the raw pixel values and encodes the complete set of dependencies in the image. Architectural novelties include fast two-dimensional recurrent layers and an effective use of residual connections in deep recurrent networks. We achieve log-likelihood scores on natural images that are considerably better than the previous state of the art. Our main results also provide benchmarks on the diverse ImageNet dataset. Samples generated from the model appear crisp, varied and globally coherent.