# Revisiting Likelihood-Based Out-of-Distribution Detection by Modeling Representations

arXiv: https://arxiv.org/abs/2504.07793 · HTML: https://mlsanity.com/paper/2504.07793/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 27 of 27)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [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)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [ReAct: Out-of-distribution Detection With Rectified Activations](https://mlsanity.com/paper/2111.12797/) (2021)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [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)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [OpenOOD v1.5: Enhanced Benchmark for Out-of-Distribution Detection](https://mlsanity.com/paper/2306.09301/) (2023)
- [Benchmarking Self-Supervised Learning on Diverse Pathology Datasets](https://mlsanity.com/paper/2212.04690/) (2022)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Understanding Failures in Out-of-Distribution Detection with Deep Generative Models](https://mlsanity.com/paper/2107.06908/) (2021)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [IntroVAE: Introspective Variational Autoencoders for Photographic Image Synthesis](https://mlsanity.com/paper/1807.06358/) (2018)
- [Soft-IntroVAE: Analyzing and Improving the Introspective Variational Autoencoder](https://mlsanity.com/paper/2012.13253/) (2020)
- [Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.17432/) (2023)

## Built on by (most cited first, 6 of 6)

- [EigenScore: OOD Detection using Covariance in Diffusion Models](https://mlsanity.com/paper/2510.07206/) (2025)
- [Enhancing Out-of-Distribution Detection with Extended Logit Normalization](https://mlsanity.com/paper/2504.11434/) (2025)
- [Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning](https://mlsanity.com/paper/2605.05638/) (2026)
- [Out-of-Distribution Detection in Molecular Complexes via Diffusion Models for Irregular Graphs](https://mlsanity.com/paper/2512.18454/) (2025)
- [Backbone-Equated Diffusion OOD via Sparse Internal Snapshots](https://mlsanity.com/paper/2605.11014/) (2026)
- [Tippett-minimum Fusion of Representation-space Diffusion Models for Multi-Encoder Out-of-Distribution Detection](https://mlsanity.com/paper/2605.20502/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is critical for ensuring the reliability of deep learning systems, particularly in safety-critical applications. Likelihood-based deep generative models have historically faced criticism for their unsatisfactory performance in OOD detection, often assigning higher likelihood to OOD data than in-distribution samples when applied to image data. In this work, we demonstrate that likelihood is not inherently flawed. Rather, several properties in the images space prohibit likelihood as a valid detection score. Given a sufficiently good likelihood estimator, specifically using the probability flow formulation of a diffusion model, we show that likelihood-based methods can still perform on par with state-of-the-art methods when applied in the representation space of pre-trained encoders. The code of our work can be found at hrefhttps://github.com/limchaos/Likelihood-OOD.gittexttthttps://github.com/limchaos/Likelihood-OOD.git.