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

Brett Barkley, Preston Culbertson, David Fridovich-Keil

TL;DR

SCOPED addresses the critical need for fast, reliable OOD detection for diffusion models by exploiting theScore-Curvature Ratio, a statistic that combines score norm and local curvature. By estimating the curvature with Hutchinson’s trace estimator and evaluating at a few strategically chosen noise levels, SCOPED achieves substantial reductions in forward passes while maintaining competitive AUROC across vision benchmarks and robust separation in RL tasks. Calibration via kernel density estimation on in-distribution statistics enables fully unsupervised deployment, with offline selection of diffusion steps ensuring robustness without OOD tuning. The results demonstrate that a geometry-driven, information-theoretic approach can deliver practical, scalable OOD detection with broad applicability to perception, control, and data curation.

Abstract

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.

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

TL;DR

SCOPED addresses the critical need for fast, reliable OOD detection for diffusion models by exploiting theScore-Curvature Ratio, a statistic that combines score norm and local curvature. By estimating the curvature with Hutchinson’s trace estimator and evaluating at a few strategically chosen noise levels, SCOPED achieves substantial reductions in forward passes while maintaining competitive AUROC across vision benchmarks and robust separation in RL tasks. Calibration via kernel density estimation on in-distribution statistics enables fully unsupervised deployment, with offline selection of diffusion steps ensuring robustness without OOD tuning. The results demonstrate that a geometry-driven, information-theoretic approach can deliver practical, scalable OOD detection with broad applicability to perception, control, and data curation.

Abstract

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.

Paper Structure

This paper contains 36 sections, 16 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Score-Based Diffusion Models
  4. Typicality as a Measure of OOD
  5. The Score-Curvature Ratio
  6. From the Score-Curvature Ratio to a Practical OOD Metric: SCOPED
  7. Achieving Computational Efficiency
  8. Motivation and OOD Detection with Kernel Density Estimation
  9. Motivating example in reinforcement learning.
  10. Calibration for a practical detector.
  11. Offline Selection of Noise Levels for SCOPED
  12. Related Work
  13. Results
  14. Reinforcement Learning Case Studies
  15. DMC results.
  16. ...and 21 more sections

Figures (3)

  • Figure 1: Distribution of SCOPED OOD scores $T(x)$ for humanoid-stand and humanoid-walk transitions. In-distribution evaluations concentrate near $1$ with tight quantiles, while cross-task evaluations shift upward and become more dispersed, indicating separability.
  • Figure 2: AUROC heatmaps for D4RL. Rows indicate the training buffer and columns the OOD buffer. D4RL data is abbreviated R (random), M (medium), E (expert), and MR (medium-replay).
  • Figure 3: Signal-to-noise ratio curve for CIFAR-10. The fraction of signal retained under the forward diffusion process decays steadily with timestep. Early timesteps preserve fine image detail, while later ones become noise-dominated.

Theorems & Definitions (1)

  • Definition 1: $\delta$-OOD points