# SCOPED: Score-Curvature Out-of-distribution Proximity Evaluator for Diffusion

arXiv: https://arxiv.org/abs/2510.01456 · HTML: https://mlsanity.com/paper/2510.01456/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [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)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [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)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models](https://mlsanity.com/paper/2010.00654/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Synthetic Experience Replay](https://mlsanity.com/paper/2303.06614/) (2023)
- [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)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Unsupervised Brain Anomaly Detection and Segmentation with Transformers](https://mlsanity.com/paper/2102.11650/) (2021)
- [Out-of-Distribution Detection with a Single Unconditional Diffusion Model](https://mlsanity.com/paper/2405.11881/) (2024)
- [Out-of-Distribution Detection Methods Answer the Wrong Questions](https://mlsanity.com/paper/2507.01831/) (2025)

## Built on by (most cited first, 3 of 3)

- [GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models](https://mlsanity.com/paper/2602.00191/) (2026)
- [Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning](https://mlsanity.com/paper/2605.05638/) (2026)
- [Backbone-Equated Diffusion OOD via Sparse Internal Snapshots](https://mlsanity.com/paper/2605.11014/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection is essential for reliable deployment of machine learning systems in vision, robotics, reinforcement learning, and beyond. We introduce Score-Curvature Out-of-distribution Proximity Evaluator for Diffusion (SCOPED), a fast and general-purpose OOD detection method for diffusion models that reduces the number of forward passes on the trained model by an order of magnitude compared to prior methods, outperforming most diffusion-based baselines and closely approaching the accuracy of the strongest ones. SCOPED is computed from a single diffusion model trained once on a diverse dataset, and combines the Jacobian trace and squared norm of the model's score function into a single test statistic. Rather than thresholding on a fixed value, we estimate the in-distribution density of SCOPED scores using kernel density estimation, enabling a flexible, unsupervised test that, in the simplest case, only requires a single forward pass and one Jacobian-vector product (JVP), made efficient by Hutchinson's trace estimator. On four vision benchmarks, SCOPED achieves competitive or state-of-the-art precision-recall scores despite its low computational cost. The same method generalizes to robotic control tasks with shared state and action spaces, identifying distribution shifts across reward functions and training regimes. These results position SCOPED as a practical foundation for fast and reliable OOD detection in real-world domains, including perceptual artifacts in vision, outlier detection in autoregressive models, exploration in reinforcement learning, and dataset curation for unsupervised training.