# ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models

arXiv: https://arxiv.org/abs/2301.04257 · HTML: https://mlsanity.com/paper/2301.04257/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 65 references that are in the map.
- First posted on arXiv 11 Jan 2023.

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

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [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)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [GS-WGAN: A Gradient-Sanitized Approach for Learning Differentially Private Generators](https://mlsanity.com/paper/2006.08265/) (2020)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [CTAB-GAN+: Enhancing Tabular Data Synthesis](https://mlsanity.com/paper/2204.00401/) (2022)
- [Perfect density models cannot guarantee anomaly detection](https://mlsanity.com/paper/2012.03808/) (2020)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)

## Built on by (most cited first, 7 of 7)

- [GradStop: Exploring Training Dynamics in Unsupervised Outlier Detection through Gradient](https://mlsanity.com/paper/2412.08501/) (2024)
- [ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effect](https://mlsanity.com/paper/2408.09791/) (2024)
- [Memorize Early, Then Query: Inlier-Memorization-Guided Active Outlier Detection](https://mlsanity.com/paper/2601.10993/) (2026)
- [Time-dependent density estimation using binary classifiers](https://mlsanity.com/paper/2506.15505/) (2025)
- [UniOD: A Universal Model for Outlier Detection across Diverse Domains](https://mlsanity.com/paper/2507.06624/) (2025)
- [What Drives the Inlier-Memorization Effect? A Theory of Outlier Detection via Early Training Dynamics](https://mlsanity.com/paper/2606.29791/) (2026)
- [CORE: In-Context Reconstruction for Unified Tabular Anomaly Detection](https://mlsanity.com/paper/2607.27615/) (2026)

## Abstract (arXiv)

The unsupervised outlier detection (UOD) problem refers to a task to identify inliers given training data which contain outliers as well as inliers, without any labeled information about inliers and outliers. It has been widely recognized that using fully-trained likelihood-based deep generative models (DGMs) often results in poor performance in distinguishing inliers from outliers. In this study, we claim that the likelihood itself could serve as powerful evidence for identifying inliers in UOD tasks, provided that DGMs are carefully under-fitted. Our approach begins with a novel observation called the inlier-memorization (IM) effect-when training a deep generative model with data including outliers, the model initially memorizes inliers before outliers. Based on this finding, we develop a new method called the outlier detection via the IM effect (ODIM). Remarkably, the ODIM requires only a few updates, making it computationally efficient-at least tens of times faster than other deep-learning-based algorithms. Also, the ODIM filters out outliers excellently, regardless of the data type, including tabular, image, and text data. To validate the superiority and efficiency of our method, we provide extensive empirical analyses on close to 60 datasets.