# Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2310.17432 · HTML: https://mlsanity.com/paper/2310.17432/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (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)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [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)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Improving Reconstruction Autoencoder Out-of-distribution Detection with Mahalanobis Distance](https://mlsanity.com/paper/1812.02765/) (2018)
- [Density of States Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2006.09273/) (2020)
- [Unsupervised Out-of-Distribution Detection with Diffusion Inpainting](https://mlsanity.com/paper/2302.10326/) (2023)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [On the Out-of-distribution Generalization of Probabilistic Image Modelling](https://mlsanity.com/paper/2109.02639/) (2021)
- [Detecting Out-of-distribution Samples via Variational Auto-encoder with Reliable Uncertainty Estimation](https://mlsanity.com/paper/2007.08128/) (2020)
- [Probabilistic Autoencoder](https://mlsanity.com/paper/2006.05479/) (2020)

## Built on by (most cited first, 10 of 10)

- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [Detecting Out-Of-Distribution Earth Observation Images with Diffusion Models](https://mlsanity.com/paper/2404.12667/) (2024)
- [Diffusion for Out-of-Distribution Detection on Road Scenes and Beyond](https://mlsanity.com/paper/2407.15739/) (2024)
- [Revisiting Likelihood-Based Out-of-Distribution Detection by Modeling Representations](https://mlsanity.com/paper/2504.07793/) (2025)
- [Probability Density from Latent Diffusion Models for Out-of-Distribution Detection](https://mlsanity.com/paper/2508.15737/) (2025)
- [Differentiable Score-Based Likelihoods: Learning CT Motion Compensation From Clean Images](https://mlsanity.com/paper/2404.14747/) (2024)
- [Resultant: Incremental Effectiveness on Likelihood for Unsupervised Out-of-Distribution Detection](https://mlsanity.com/paper/2409.03801/) (2024)
- [Out-of-Distribution Detection in Molecular Complexes via Diffusion Models for Irregular Graphs](https://mlsanity.com/paper/2512.18454/) (2025)
- [Generalization and Memorization in Rectified Flow](https://mlsanity.com/paper/2603.13421/) (2026)
- [Backbone-Equated Diffusion OOD via Sparse Internal Snapshots](https://mlsanity.com/paper/2605.11014/) (2026)

## Abstract (arXiv)

Out-of-Distribution detection between dataset pairs has been extensively explored with generative models. We show that likelihood-based Out-of-Distribution detection can be extended to diffusion models by leveraging the fact that they, like other likelihood-based generative models, are dramatically affected by the input sample complexity. Currently, all Out-of-Distribution detection methods with Diffusion Models are reconstruction-based. We propose a new likelihood ratio for Out-of-Distribution detection with Deep Denoising Diffusion Models, which we call the Complexity Corrected Likelihood Ratio. Our likelihood ratio is constructed using Evidence Lower-Bound evaluations from an individual model at various noising levels. We present results that are comparable to state-of-the-art Out-of-Distribution detection methods with generative models.