# Multiscale Score Matching for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2010.13132 · HTML: https://mlsanity.com/paper/2010.13132/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

## Built on by (most cited first, 30 of 36)

- [On the Out-of-distribution Generalization of Probabilistic Image Modelling](https://mlsanity.com/paper/2109.02639/) (2021)
- [SAFE: Sensitivity-Aware Features for Out-of-Distribution Object Detection](https://mlsanity.com/paper/2208.13930/) (2022)
- [iDECODe: In-distribution Equivariance for Conformal Out-of-distribution Detection](https://mlsanity.com/paper/2201.02331/) (2022)
- [MULDE: Multiscale Log-Density Estimation via Denoising Score Matching for Video Anomaly Detection](https://mlsanity.com/paper/2403.14497/) (2024)
- [Out-of-Distribution Detection with a Single Unconditional Diffusion Model](https://mlsanity.com/paper/2405.11881/) (2024)
- [Igeood: An Information Geometry Approach to Out-of-Distribution Detection](https://mlsanity.com/paper/2203.07798/) (2022)
- [FOOGD: Federated Collaboration for Both Out-of-distribution Generalization and Detection](https://mlsanity.com/paper/2410.11397/) (2024)
- [Likelihood-based Out-of-Distribution Detection with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.17432/) (2023)
- [Projection Regret: Reducing Background Bias for Novelty Detection via Diffusion Models](https://mlsanity.com/paper/2312.02615/) (2023)
- [Diffusion for Out-of-Distribution Detection on Road Scenes and Beyond](https://mlsanity.com/paper/2407.15739/) (2024)
- [Task Agnostic and Post-hoc Unseen Distribution Detection](https://mlsanity.com/paper/2207.13083/) (2022)
- [ODIM: Outlier Detection via Likelihood of Under-Fitted Generative Models](https://mlsanity.com/paper/2301.04257/) (2023)
- [Towards Robust Active Feature Acquisition](https://mlsanity.com/paper/2107.04163/) (2021)
- [Out-of-Distribution Detection with Class Ratio Estimation](https://mlsanity.com/paper/2206.03955/) (2022)
- [Proto-OOD: Enhancing OOD Object Detection with Prototype Feature Similarity](https://mlsanity.com/paper/2409.05466/) (2024)
- [Redesigning Out-of-Distribution Detection on 3D Medical Images](https://mlsanity.com/paper/2308.07324/) (2023)
- [Distribution Guided Active Feature Acquisition](https://mlsanity.com/paper/2410.03915/) (2024)
- [SCOPED: Score-Curvature Out-of-distribution Proximity Evaluator for Diffusion](https://mlsanity.com/paper/2510.01456/) (2025)
- [Natural Attribute-based Shift Detection](https://mlsanity.com/paper/2110.09276/) (2021)
- [A Functional Data Perspective and Baseline On Multi-Layer Out-of-Distribution Detection](https://mlsanity.com/paper/2306.03522/) (2023)
- [Zero-Shot Image Anomaly Detection Using Generative Foundation Models](https://mlsanity.com/paper/2507.22692/) (2025)
- [Geometry over Density: Few-Shot Cross-Domain OOD Detection](https://mlsanity.com/paper/2605.03410/) (2026)
- [Mitigating Out-of-Distribution Data Density Overestimation in Energy-Based Models](https://mlsanity.com/paper/2205.14817/) (2022)
- [Anomaly Detection via Gumbel Noise Score Matching](https://mlsanity.com/paper/2304.03220/) (2023)
- [ScoreCL: Augmentation-Adaptive Contrastive Learning via Score-Matching Function](https://mlsanity.com/paper/2306.04175/) (2023)
- [GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models](https://mlsanity.com/paper/2602.00191/) (2026)
- [Generative Inverse Design with Abstention via Diagonal Flow Matching](https://mlsanity.com/paper/2603.15925/) (2026)
- [Beyond Prompts: Unconditional 3D Inversion for Out-of-Distribution Shapes](https://mlsanity.com/paper/2604.14914/) (2026)
- [Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning](https://mlsanity.com/paper/2605.05638/) (2026)
- [Solving Sample-Level Out-of-Distribution Detection on 3D Medical Images](https://mlsanity.com/paper/2212.06506/) (2022)

## Abstract (arXiv)

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.