# Structured Uncertainty Prediction Networks

arXiv: https://arxiv.org/abs/1802.07079 · HTML: https://mlsanity.com/paper/1802.07079/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

## Built on by (most cited first, 30 of 34)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance](https://mlsanity.com/paper/2402.02149/) (2024)
- [Interpretable Unsupervised Diversity Denoising and Artefact Removal](https://mlsanity.com/paper/2104.01374/) (2021)
- [A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications](https://mlsanity.com/paper/2111.01968/) (2021)
- [Collaborative Uncertainty in Multi-Agent Trajectory Forecasting](https://mlsanity.com/paper/2110.13947/) (2021)
- [Learning a Depth Covariance Function](https://mlsanity.com/paper/2303.12157/) (2023)
- [Uncertainty Quantification via Neural Posterior Principal Components](https://mlsanity.com/paper/2309.15533/) (2023)
- [Collaborative Uncertainty Benefits Multi-Agent Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2207.05195/) (2022)
- [Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems](https://mlsanity.com/paper/2102.03169/) (2021)
- [VL4Pose: Active Learning Through Out-Of-Distribution Detection For Pose Estimation](https://mlsanity.com/paper/2210.06028/) (2022)
- [Learning Structured Gaussians to Approximate Deep Ensembles](https://mlsanity.com/paper/2203.15485/) (2022)
- [Sequential keypoint density estimator: an overlooked baseline of skeleton-based video anomaly detection](https://mlsanity.com/paper/2506.18368/) (2025)
- [MILD: Multimodal Interactive Latent Dynamics for Learning Human-Robot Interaction](https://mlsanity.com/paper/2210.12418/) (2022)
- [GUPNet++: Geometry Uncertainty Propagation Network for Monocular 3D Object Detection](https://mlsanity.com/paper/2310.15624/) (2023)
- [Covariance Prediction via Convex Optimization](https://mlsanity.com/paper/2101.12416/) (2021)
- [Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariance](https://mlsanity.com/paper/2210.14586/) (2022)
- [TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression](https://mlsanity.com/paper/2310.18953/) (2023)
- [Hierarchical Uncertainty Exploration via Feedforward Posterior Trees](https://mlsanity.com/paper/2405.15719/) (2024)
- [Structured Uncertainty in the Observation Space of Variational Autoencoders](https://mlsanity.com/paper/2205.12533/) (2022)
- [Uncertainty Visualization via Low-Dimensional Posterior Projections](https://mlsanity.com/paper/2312.07804/) (2023)
- [GUIDE-VAE: Advancing Data Generation with User Information and Pattern Dictionaries](https://mlsanity.com/paper/2411.03936/) (2024)
- [Feature Hallucination for Self-supervised Action Recognition](https://mlsanity.com/paper/2506.20342/) (2025)
- [Towards Self-Supervised Covariance Estimation in Deep Heteroscedastic Regression](https://mlsanity.com/paper/2502.10587/) (2025)
- [Probabilistic bias adjustment of seasonal predictions of Arctic Sea Ice Concentration](https://mlsanity.com/paper/2510.09891/) (2025)
- [Deep priors for satellite image restoration with accurate uncertainties](https://mlsanity.com/paper/2412.04130/) (2024)
- [SAFER: A Calibrated Risk-Aware Multimodal Recommendation Model for Dynamic Treatment Regimes](https://mlsanity.com/paper/2506.06649/) (2025)
- [Toward generative machine learning for boosting ensembles of climate simulations](https://mlsanity.com/paper/2602.06287/) (2026)
- [Variational Heteroscedastic Volatility Model](https://mlsanity.com/paper/2204.05806/) (2022)
- [Likelihood-Free Variational Autoencoders](https://mlsanity.com/paper/2504.17622/) (2025)
- [Structured Uncertainty Similarity Score (SUSS): Learning a Probabilistic, Interpretable, Perceptual Metric Between Images](https://mlsanity.com/paper/2512.03701/) (2025)

## Abstract (arXiv)

This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to predict a full Gaussian covariance matrix for each reconstruction, which permits efficient sampling and likelihood evaluation. We demonstrate that our model can accurately reconstruct ground truth correlated residual distributions for synthetic datasets and generate plausible high frequency samples for real face images. We also illustrate the use of these predicted covariances for structure preserving image denoising.