# GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models

arXiv: https://arxiv.org/abs/2602.00191 · HTML: https://mlsanity.com/paper/2602.00191/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 37)

- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [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)
- [Neural Empirical Bayes](https://mlsanity.com/paper/1903.02334/) (2019)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Kernel PCA for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.02949/) (2024)
- [Out-of-Distribution Detection with a Single Unconditional Diffusion Model](https://mlsanity.com/paper/2405.11881/) (2024)
- [GradOrth: A Simple yet Efficient Out-of-Distribution Detection with Orthogonal Projection of Gradients](https://mlsanity.com/paper/2308.00310/) (2023)
- [What Affects Learned Equivariance in Deep Image Recognition Models?](https://mlsanity.com/paper/2304.02628/) (2023)

## Built on by (most cited first, 1 of 1)

- [Backbone-Equated Diffusion OOD via Sparse Internal Snapshots](https://mlsanity.com/paper/2605.11014/) (2026)

## Abstract (arXiv)

Diffusion models learn a time-indexed score field sθ(xt,t) that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group G, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual, which averages an equivariance-residual functional over G, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. Code is available at https://github.com/RouzAY/gepc-diffusion/.