# PixelPyramids: Exact Inference Models from Lossless Image Pyramids

arXiv: https://arxiv.org/abs/2110.08787 · HTML: https://mlsanity.com/paper/2110.08787/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 17 Oct 2021.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [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)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [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)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks](https://mlsanity.com/paper/1506.05751/) (2015)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [PixelSNAIL: An Improved Autoregressive Generative Model](https://mlsanity.com/paper/1712.09763/) (2017)
- [Density Modeling of Images using a Generalized Normalization Transformation](https://mlsanity.com/paper/1511.06281/) (2015)
- [Hierarchical Generative Modeling for Controllable Speech Synthesis](https://mlsanity.com/paper/1810.07217/) (2018)
- [Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscaling](https://mlsanity.com/paper/1812.01608/) (2018)
- [Parallel Multiscale Autoregressive Density Estimation](https://mlsanity.com/paper/1703.03664/) (2017)

## Built on by (most cited first, 1 of 1)

- [Zero-Shot Detection of AI-Generated Images](https://mlsanity.com/paper/2409.15875/) (2024)

## Abstract (arXiv)

Autoregressive models are a class of exact inference approaches with highly flexible functional forms, yielding state-of-the-art density estimates for natural images. Yet, the sequential ordering on the dimensions makes these models computationally expensive and limits their applicability to low-resolution imagery. In this work, we propose Pixel-Pyramids, a block-autoregressive approach employing a lossless pyramid decomposition with scale-specific representations to encode the joint distribution of image pixels. Crucially, it affords a sparser dependency structure compared to fully autoregressive approaches. Our PixelPyramids yield state-of-the-art results for density estimation on various image datasets, especially for high-resolution data. For CelebA-HQ 1024 x 1024, we observe that the density estimates (in terms of bits/dim) are improved to ~44% of the baseline despite sampling speeds superior even to easily parallelizable flow-based models.