# On Inverse Problems, Parameter Estimation, and Domain Generalization

arXiv: https://arxiv.org/abs/2506.06024 · HTML: https://mlsanity.com/paper/2506.06024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 73 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Dirty Pixels: Towards End-to-End Image Processing and Perception](https://mlsanity.com/paper/1701.06487/) (2017)
- [Deep Learning for Wireless Communications](https://mlsanity.com/paper/2005.06068/) (2020)
- [Evaluating Robustness of Deep Image Super-Resolution against Adversarial Attacks](https://mlsanity.com/paper/1904.06097/) (2019)
- [Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration](https://mlsanity.com/paper/2410.00418/) (2024)
- [Fairness for Image Generation with Uncertain Sensitive Attributes](https://mlsanity.com/paper/2106.12182/) (2021)
- [AnyStar: Domain randomized universal star-convex 3D instance segmentation](https://mlsanity.com/paper/2307.07044/) (2023)
- [Towards Adversarially Robust Deep Image Denoising](https://mlsanity.com/paper/2201.04397/) (2022)
- [Reasons for the Superiority of Stochastic Estimators over Deterministic Ones: Robustness, Consistency and Perceptual Quality](https://mlsanity.com/paper/2211.08944/) (2022)
- [The harms of class imbalance corrections for machine learning based prediction models: a simulation study](https://mlsanity.com/paper/2404.19494/) (2024)
- [Deep Image Destruction: Vulnerability of Deep Image-to-Image Models against Adversarial Attacks](https://mlsanity.com/paper/2104.15022/) (2021)
- [The Perception-Robustness Tradeoff in Deterministic Image Restoration](https://mlsanity.com/paper/2311.09253/) (2023)
- [Enhanced ASR Robustness to Packet Loss with a Front-End Adaptation Network](https://mlsanity.com/paper/2406.18928/) (2024)
- [Unveiling and Mitigating Adversarial Vulnerabilities in Iterative Optimizers](https://mlsanity.com/paper/2504.19000/) (2025)
- [Convolutional Sparse Coding Fast Approximation with Application to Seismic Reflectivity Estimation](https://mlsanity.com/paper/2106.15296/) (2021)
- [Domain-Aware Few-Shot Learning for Optical Coherence Tomography Noise Reduction](https://mlsanity.com/paper/2306.08102/) (2023)
- [One-Shot Image Restoration](https://mlsanity.com/paper/2404.17426/) (2024)
- [Support detection in super-resolution](https://mlsanity.com/paper/1302.3921/) (2013)
- [MBSS-T1: Model-Based Subject-Specific Self-Supervised Motion Correction for Robust Cardiac T1 Mapping](https://mlsanity.com/paper/2408.11992/) (2024)
- [AI-based Clinical Assessment of Optic Nerve Head Robustness Superseding Biomechanical Testing](https://mlsanity.com/paper/2206.04689/) (2022)
- [Self2Seg: Single-Image Self-Supervised Joint Segmentation and Denoising](https://mlsanity.com/paper/2309.10511/) (2023)

## Abstract (arXiv)

Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all physical applications, normally executed prior to downstream tasks that often involve parameter estimation. In this work, we propose a general framework for theoretical analysis of parameter estimation in inverse problem settings. We distinguish between continuous and discrete parameter estimation, corresponding with regression and classification problems, respectively. We investigate this setting for invertible and non-invertible degradation processes, with parameter estimation that is executed directly from the observed measurements, comparing with parameter estimation after data-processing performing an inversion of the observations. Our theoretical findings align with the well-known information-theoretic data processing inequality, and to a certain degree question the common misconception that data-processing for inversion, based on modern generative models that may often produce outstanding perceptual quality, will necessarily improve the following parameter estimation objective. Importantly, by re-formulating the domain-shift problem in direct relation with discrete parameter estimation, we expose a significant vulnerability in current popular practical attempts to enforce domain generalization, which we dubbed the Double Meaning Theorem. These theoretical findings are experimentally illustrated for domain shift examples in image deblurring and speckle suppression in medical imaging. It is our hope that this paper will provide practitioners with deeper insights that may be leveraged in the future for the development of more efficient and informed strategic system planning, critical in safety-sensitive applications.