# Semantic uncertainty intervals for disentangled latent spaces

arXiv: https://arxiv.org/abs/2207.10074 · HTML: https://mlsanity.com/paper/2207.10074/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 54 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation](https://mlsanity.com/paper/2011.12799/) (2020)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Semantic Photo Manipulation with a Generative Image Prior](https://mlsanity.com/paper/2005.07727/) (2020)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Collaborative Learning for Faster StyleGAN Embedding](https://mlsanity.com/paper/2007.01758/) (2020)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [Score-Based Generative Classifiers](https://mlsanity.com/paper/2110.00473/) (2021)
- [Cautious Deep Learning](https://mlsanity.com/paper/1805.09460/) (2018)
- [High Perceptual Quality Image Denoising with a Posterior Sampling CGAN](https://mlsanity.com/paper/2103.04192/) (2021)

## Built on by (most cited first, 22 of 22)

- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Federated Conformal Predictors for Distributed Uncertainty Quantification](https://mlsanity.com/paper/2305.17564/) (2023)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [On the Posterior Distribution in Denoising: Application to Uncertainty Quantification](https://mlsanity.com/paper/2309.13598/) (2023)
- [Fast yet Safe: Early-Exiting with Risk Control](https://mlsanity.com/paper/2405.20915/) (2024)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Generative Uncertainty in Diffusion Models](https://mlsanity.com/paper/2502.20946/) (2025)
- [Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models](https://mlsanity.com/paper/2311.13628/) (2023)
- [Uncertainty Quantification via Neural Posterior Principal Components](https://mlsanity.com/paper/2309.15533/) (2023)
- [From Posterior Sampling to Meaningful Diversity in Image Restoration](https://mlsanity.com/paper/2310.16047/) (2023)
- [Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models](https://mlsanity.com/paper/2405.16475/) (2024)
- [Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction](https://mlsanity.com/paper/2405.18527/) (2024)
- [What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problems](https://mlsanity.com/paper/2211.15211/) (2022)
- [Statistical Methods in Generative AI](https://mlsanity.com/paper/2509.07054/) (2025)
- [Uncertainty Visualization via Low-Dimensional Posterior Projections](https://mlsanity.com/paper/2312.07804/) (2023)
- [Metric-Guided Conformal Bounds for Probabilistic Image Reconstruction](https://mlsanity.com/paper/2404.15274/) (2024)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processing](https://mlsanity.com/paper/2512.09806/) (2025)
- [An In-Depth Examination of Risk Assessment in Multi-Class Classification Algorithms](https://mlsanity.com/paper/2412.04166/) (2024)
- [QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems](https://mlsanity.com/paper/2507.14760/) (2025)

## Abstract (arXiv)

Meaningful uncertainty quantification in computer vision requires reasoning about semantic information -- say, the hair color of the person in a photo or the location of a car on the street. To this end, recent breakthroughs in generative modeling allow us to represent semantic information in disentangled latent spaces, but providing uncertainties on the semantic latent variables has remained challenging. In this work, we provide principled uncertainty intervals that are guaranteed to contain the true semantic factors for any underlying generative model. The method does the following: (1) it uses quantile regression to output a heuristic uncertainty interval for each element in the latent space (2) calibrates these uncertainties such that they contain the true value of the latent for a new, unseen input. The endpoints of these calibrated intervals can then be propagated through the generator to produce interpretable uncertainty visualizations for each semantic factor. This technique reliably communicates semantically meaningful, principled, and instance-adaptive uncertainty in inverse problems like image super-resolution and image completion.