# HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Model

arXiv: https://arxiv.org/abs/2510.05054 · HTML: https://mlsanity.com/paper/2510.05054/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 58 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Hybrid Models with Deep and Invertible Features](https://mlsanity.com/paper/1902.02767/) (2019)
- [Structured Output Learning with Conditional Generative Flows](https://mlsanity.com/paper/1905.13288/) (2019)
- [Will Artificial Intelligence supersede Earth System and Climate Models?](https://mlsanity.com/paper/2101.09126/) (2021)
- [Faithful Heteroscedastic Regression with Neural Networks](https://mlsanity.com/paper/2212.09184/) (2022)
- [Label-wise Aleatoric and Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2406.02354/) (2024)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Monte Carlo DropBlock for Modelling Uncertainty in Object Detection](https://mlsanity.com/paper/2108.03614/) (2021)
- [From Aleatoric to Epistemic: Exploring Uncertainty Quantification Techniques in Artificial Intelligence](https://mlsanity.com/paper/2501.03282/) (2025)
- [Explainability through uncertainty: Trustworthy decision-making with neural networks](https://mlsanity.com/paper/2403.10168/) (2024)

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

- [Rethinking Uncertainty Quantification and Entanglement in Image Segmentation](https://mlsanity.com/paper/2603.18792/) (2026)
- [Density-Informed Pseudo-Counts for Calibrated Evidential Deep Learning](https://mlsanity.com/paper/2602.01477/) (2026)
- [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://mlsanity.com/paper/2607.28248/) (2026)

## Abstract (arXiv)

Uncertainty quantification is critical for ensuring robustness in high-stakes machine learning applications. We introduce HybridFlow, a modular hybrid architecture that unifies the modeling of aleatoric and epistemic uncertainty by combining a Conditional Masked Autoregressive normalizing flow for estimating aleatoric uncertainty with a flexible probabilistic predictor for epistemic uncertainty. The framework supports integration with any probabilistic model class, allowing users to easily adapt HybridFlow to existing architectures without sacrificing predictive performance. HybridFlow improves upon previous uncertainty quantification frameworks across a range of regression tasks, such as depth estimation, a collection of regression benchmarks, and a scientific case study of ice sheet emulation. We also provide empirical results of the quantified uncertainty, showing that the uncertainty quantified by HybridFlow is calibrated and better aligns with model error than existing methods for quantifying aleatoric and epistemic uncertainty. HybridFlow addresses a key challenge in Bayesian deep learning, unifying aleatoric and epistemic uncertainty modeling in a single robust framework.