# On the Out-of-distribution Generalization of Probabilistic Image Modelling

arXiv: https://arxiv.org/abs/2109.02639 · HTML: https://mlsanity.com/paper/2109.02639/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 4 Sep 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [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 Anomaly Detection with Deep Invertible Networks through Hierarchies of Distributions and Features](https://mlsanity.com/paper/2006.10848/) (2020)
- [Bit-Swap: Recursive Bits-Back Coding for Lossless Compression with Hierarchical Latent Variables](https://mlsanity.com/paper/1905.06845/) (2019)
- [Detecting semantic anomalies](https://mlsanity.com/paper/1908.04388/) (2019)
- [Uncertainty in the Variational Information Bottleneck](https://mlsanity.com/paper/1807.00906/) (2018)
- [HiLLoC: Lossless Image Compression with Hierarchical Latent Variable Models](https://mlsanity.com/paper/1912.09953/) (2019)
- [IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression](https://mlsanity.com/paper/2006.12459/) (2020)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Compression with Flows via Local Bits-Back Coding](https://mlsanity.com/paper/1905.08500/) (2019)
- [Detecting Out-of-Distribution Examples with In-distribution Examples and Gram Matrices](https://mlsanity.com/paper/1912.12510/) (2019)

## Built on by (most cited first, 30 of 33)

- [NIRVANA: Neural Implicit Representations of Videos with Adaptive Networks and Autoregressive Patch-wise Modeling](https://mlsanity.com/paper/2212.14593/) (2022)
- [Lossy Image Compression with Quantized Hierarchical VAEs](https://mlsanity.com/paper/2208.13056/) (2022)
- [QARV: Quantization-Aware ResNet VAE for Lossy Image Compression](https://mlsanity.com/paper/2302.08899/) (2023)
- [Domain Generalization through Meta-Learning: A Survey](https://mlsanity.com/paper/2404.02785/) (2024)
- [Augmenting Softmax Information for Selective Classification with Out-of-Distribution Data](https://mlsanity.com/paper/2207.07506/) (2022)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Tackling Structural Hallucination in Image Translation with Local Diffusion](https://mlsanity.com/paper/2404.05980/) (2024)
- [Lossless Compression with Probabilistic Circuits](https://mlsanity.com/paper/2111.11632/) (2021)
- [CLUTR: Curriculum Learning via Unsupervised Task Representation Learning](https://mlsanity.com/paper/2210.10243/) (2022)
- [On the Usefulness of Deep Ensemble Diversity for Out-of-Distribution Detection](https://mlsanity.com/paper/2207.07517/) (2022)
- [Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching](https://mlsanity.com/paper/2406.10808/) (2024)
- [A Likelihood Ratio-Based Approach to Segmenting Unknown Objects](https://mlsanity.com/paper/2409.06424/) (2024)
- [Your Finetuned Large Language Model is Already a Powerful Out-of-distribution Detector](https://mlsanity.com/paper/2404.08679/) (2024)
- [Tackling Hallucination from Conditional Models for Medical Image Reconstruction with DynamicDPS](https://mlsanity.com/paper/2503.01075/) (2025)
- [Generalization Gap in Amortized Inference](https://mlsanity.com/paper/2205.11640/) (2022)
- [Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.17432/) (2023)
- [Latent-INR: A Flexible Framework for Implicit Representations of Videos with Discriminative Semantics](https://mlsanity.com/paper/2408.02672/) (2024)
- [Forte : Finding Outliers with Representation Typicality Estimation](https://mlsanity.com/paper/2410.01322/) (2024)
- [Falsehoods that ML researchers believe about OOD detection](https://mlsanity.com/paper/2210.12767/) (2022)
- [Improving VAE-based Representation Learning](https://mlsanity.com/paper/2205.14539/) (2022)
- [CALLIC: Content Adaptive Learning for Lossless Image Compression](https://mlsanity.com/paper/2412.17464/) (2024)
- [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)
- [Vision Checklist: Towards Testable Error Analysis of Image Models to Help System Designers Interrogate Model Capabilities](https://mlsanity.com/paper/2201.11674/) (2022)
- [Out-of-Distribution Detection with Class Ratio Estimation](https://mlsanity.com/paper/2206.03955/) (2022)
- [Approximations to the Fisher Information Metric of Deep Generative Models for Out-Of-Distribution Detection](https://mlsanity.com/paper/2403.01485/) (2024)
- [High-Frequency Enhanced Hybrid Neural Representation for Video Compression](https://mlsanity.com/paper/2411.06685/) (2024)
- [SIEDD: Shared-Implicit Encoder with Discrete Decoders](https://mlsanity.com/paper/2506.23382/) (2025)
- [SR-OOD: Out-of-Distribution Detection via Sample Repairing](https://mlsanity.com/paper/2305.18228/) (2023)

## Abstract (arXiv)

Out-of-distribution (OOD) detection and lossless compression constitute two problems that can be solved by the training of probabilistic models on a first dataset with subsequent likelihood evaluation on a second dataset, where data distributions differ. By defining the generalization of probabilistic models in terms of likelihood we show that, in the case of image models, the OOD generalization ability is dominated by local features. This motivates our proposal of a Local Autoregressive model that exclusively models local image features towards improving OOD performance. We apply the proposed model to OOD detection tasks and achieve state-of-the-art unsupervised OOD detection performance without the introduction of additional data. Additionally, we employ our model to build a new lossless image compressor: NeLLoC (Neural Local Lossless Compressor) and report state-of-the-art compression rates and model size.