# On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods

arXiv: https://arxiv.org/abs/2605.13146 · HTML: https://mlsanity.com/paper/2605.13146/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 62 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 27 of 27)

- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Scaling Out-of-Distribution Detection for Real-World Settings](https://mlsanity.com/paper/1911.11132/) (2019)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [How I failed machine learning in medical imaging -- shortcomings and recommendations](https://mlsanity.com/paper/2103.10292/) (2021)
- [Hallucination Index: An Image Quality Metric for Generative Reconstruction Models](https://mlsanity.com/paper/2407.12780/) (2024)
- [Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Prior](https://mlsanity.com/paper/2008.08837/) (2020)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Adversarial Robustness of MR Image Reconstruction under Realistic Perturbations](https://mlsanity.com/paper/2208.03161/) (2022)
- [Tackling Hallucination from Conditional Models for Medical Image Reconstruction with DynamicDPS](https://mlsanity.com/paper/2503.01075/) (2025)
- [On the Learnability of Out-of-distribution Detection](https://mlsanity.com/paper/2404.04865/) (2024)
- [A robust and scalable framework for hallucination detection in virtual tissue staining and digital pathology](https://mlsanity.com/paper/2404.18458/) (2024)
- [Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems](https://mlsanity.com/paper/2407.17667/) (2024)
- [Mining the manifolds of deep generative models for multiple data-consistent solutions of ill-posed tomographic imaging problems](https://mlsanity.com/paper/2202.05311/) (2022)
- [Ground-based image deconvolution with Swin Transformer UNet](https://mlsanity.com/paper/2405.07842/) (2024)
- [DARDA: Domain-Aware Real-Time Dynamic Neural Network Adaptation](https://mlsanity.com/paper/2409.09753/) (2024)
- [Average Kernel Sizes -- Computable Sharp Accuracy Bounds for Inverse Problems](https://mlsanity.com/paper/2510.10229/) (2025)
- [CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processing](https://mlsanity.com/paper/2512.09806/) (2025)

## Abstract (arXiv)

Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic-looking but incorrect details, undermining their reliability, especially when ground truth data is unavailable. We develop a theoretical framework showing that such hallucinations are not merely artifacts of particular models, but can arise from the ill-posed nature of the inverse problem itself. We derive necessary and sufficient conditions for hallucinations, together with computable bounds on their magnitude that depend only on the forward model. Building on this theory, we introduce algorithms to: (1) estimate the minimum hallucination magnitude achievable by any reconstruction model for a given input; (2) assess the faithfulness of reconstructed details by a given reconstruction model. Experiments across three imaging tasks demonstrate that our approach applies broadly, including to modern generative models, and provides a principled way to quantify and evaluate AI hallucinations.