# Geometry over Density: Few-Shot Cross-Domain OOD Detection

arXiv: https://arxiv.org/abs/2605.03410 · HTML: https://mlsanity.com/paper/2605.03410/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 30 of 35)

- [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 Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [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)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Delving into Out-of-Distribution Detection with Vision-Language Representations](https://mlsanity.com/paper/2211.13445/) (2022)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [Zero-Shot Out-of-Distribution Detection Based on the Pre-trained Model CLIP](https://mlsanity.com/paper/2109.02748/) (2021)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (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)
- [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)
- [Panoptic Scene Graph Generation with Semantics-Prototype Learning](https://mlsanity.com/paper/2307.15567/) (2023)
- [Multiscale Score Matching for Out-of-Distribution Detection](https://mlsanity.com/paper/2010.13132/) (2020)
- [Treble Counterfactual VLMs: A Causal Approach to Hallucination](https://mlsanity.com/paper/2503.06169/) (2025)
- [TS-Reasoner: Domain-Oriented Time Series Inference Agents for Reasoning and Automated Analysis](https://mlsanity.com/paper/2410.04047/) (2024)
- [DPU: Dynamic Prototype Updating for Multimodal Out-of-Distribution Detection](https://mlsanity.com/paper/2411.08227/) (2024)
- [Out-of-Distribution Detection with a Single Unconditional Diffusion Model](https://mlsanity.com/paper/2405.11881/) (2024)
- [Secure On-Device Video OOD Detection Without Backpropagation](https://mlsanity.com/paper/2503.06166/) (2025)
- [MetaOOD: Automatic Selection of OOD Detection Models](https://mlsanity.com/paper/2410.03074/) (2024)
- [Charts Are Not Images: On the Challenges of Scientific Chart Editing](https://mlsanity.com/paper/2512.00752/) (2025)

## Built on by (most cited first, 2 of 2)

- [JigShape: Evaluating Visual-Geometric Reasoning in VLMs through Jigsaw Puzzles](https://mlsanity.com/paper/2607.27670/) (2026)
- [Controlled Decoding Attacks on Black-Box LLMs](https://mlsanity.com/paper/2609.36956/) (2026)

## Abstract (arXiv)

Out-of-distribution (OOD) detection identifies test samples that fall outside a model's training distribution, a capability critical for safe deployment in high-stakes applications. Standard OOD detectors are trained on a specific in-distribution (ID) dataset and detect deviations from that single domain. In contrast, we study few-shot cross-domain OOD detection: given a single pre-trained model, can we perform OOD detection on arbitrary new ID-OOD task pairs using only a handful of ID samples at inference time, with no additional training? We propose UFCOD, a unified framework that achieves this goal through information-geometric analysis of diffusion trajectories. Our key insight is that diffusion noise predictions are score functions (gradients of log-density), and we extract two energy features: Path Energy (integrated score magnitude) and Dynamics Energy (score smoothness), that form a discrete Sobolev norm capturing how samples interact with the learned diffusion process. The central contribution is a train-once, deploy-anywhere paradigm: a diffusion model trained on a single dataset (e.g., CelebA) serves as a universal feature extractor for OOD detection across semantically unrelated domains (e.g., CIFAR-10, SVHN, Textures). At deployment, each new task requires only ~100 unlabeled ID samples for inference: no retraining, no fine-tuning, no task-specific adaptation. Using 100 ID samples per task, UFCOD achieves 93.7% average AUROC across 12 cross-domain benchmarks, competitive with methods trained on 50k--163k samples, demonstrating ~500× improvement in sample efficiency. See our code in https://github.com/lili0415/UFCOD.