# Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learning

arXiv: https://arxiv.org/abs/2311.06481 · HTML: https://mlsanity.com/paper/2311.06481/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 65 references that are in the map.
- First posted on arXiv 11 Nov 2023.

## Builds on (most cited first, 30 of 49)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for real-time object detectors](https://mlsanity.com/paper/2207.02696/) (2022)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [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)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Mitigating Neural Network Overconfidence with Logit Normalization](https://mlsanity.com/paper/2205.09310/) (2022)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Dropout Sampling for Robust Object Detection in Open-Set Conditions](https://mlsanity.com/paper/1710.06677/) (2017)
- [Hybrid Models for Open Set Recognition](https://mlsanity.com/paper/2003.12506/) (2020)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Unknown-Aware Object Detection: Learning What You Don't Know from Videos in the Wild](https://mlsanity.com/paper/2203.03800/) (2022)
- [BayesOD: A Bayesian Approach for Uncertainty Estimation in Deep Object Detectors](https://mlsanity.com/paper/1903.03838/) (2019)
- [Resampled Priors for Variational Autoencoders](https://mlsanity.com/paper/1810.11428/) (2018)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)

## Built on by (most cited first, 7 of 7)

- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [Evaluating Uncertainty-based Failure Detection for Closed-Loop LLM Planners](https://mlsanity.com/paper/2406.00430/) (2024)
- [Mobi-π: Mobilizing Your Robot Learning Policy](https://mlsanity.com/paper/2505.23692/) (2025)
- [FFHFlow: Diverse and Uncertainty-Aware Dexterous Grasp Generation via Flow Variational Inference](https://mlsanity.com/paper/2407.15161/) (2024)
- [Out-of-Distribution Detection for Safety Assurance of AI and Autonomous Systems](https://mlsanity.com/paper/2510.21254/) (2025)
- [SPIRIT: Perceptive Shared Autonomy for Robust Robotic Manipulation under Deep Learning Uncertainty](https://mlsanity.com/paper/2603.05111/) (2026)
- [ConFlow: Constraints-Guided Learning with Flow Matching for Motion Generation](https://mlsanity.com/paper/2607.14424/) (2026)

## Abstract (arXiv)

To facilitate reliable deployments of autonomous robots in the real world, Out-of-Distribution (OOD) detection capabilities are often required. A powerful approach for OOD detection is based on density estimation with Normalizing Flows (NFs). However, we find that prior work with NFs attempts to match the complex target distribution topologically with naive base distributions leading to adverse implications. In this work, we circumvent this topological mismatch using an expressive class-conditional base distribution trained with an information-theoretic objective to match the required topology. The proposed method enjoys the merits of wide compatibility with existing learned models without any performance degradation and minimum computation overhead while enhancing OOD detection capabilities. We demonstrate superior results in density estimation and 2D object detection benchmarks in comparison with extensive baselines. Moreover, we showcase the applicability of the method with a real-robot deployment.