# Tackling the Problem of Distributional Shifts: Correcting Misspecified, High-Dimensional Data-Driven Priors for Inverse Problems

arXiv: https://arxiv.org/abs/2407.17667 · HTML: https://mlsanity.com/paper/2407.17667/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 52 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Realistic galaxy image simulation via score-based generative models](https://mlsanity.com/paper/2111.01713/) (2021)
- [The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence](https://mlsanity.com/paper/2109.10915/) (2021)
- [Probabilistic Mass Mapping with Neural Score Estimation](https://mlsanity.com/paper/2201.05561/) (2022)
- [Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation](https://mlsanity.com/paper/2402.07808/) (2024)
- [Event-horizon-scale Imaging of M87* under Different Assumptions via Deep Generative Image Priors](https://mlsanity.com/paper/2406.02785/) (2024)
- [Radio-astronomical Image Reconstruction with Conditional Denoising Diffusion Model](https://mlsanity.com/paper/2402.10204/) (2024)
- [Diffusion-HMC: Parameter Inference with Diffusion-model-driven Hamiltonian Monte Carlo](https://mlsanity.com/paper/2405.05255/) (2024)

## Built on by (most cited first, 5 of 5)

- [Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models](https://mlsanity.com/paper/2511.04792/) (2025)
- [Optimizing Diffusion Priors in Image Reconstruction from a Single Observation](https://mlsanity.com/paper/2604.21066/) (2026)
- [MIRA: A Score for Conditional Distribution Accuracy and Model Comparison](https://mlsanity.com/paper/2605.02014/) (2026)
- [On Hallucinations in Inverse Problems: Fundamental Limits and Provable Assessment Methods](https://mlsanity.com/paper/2605.13146/) (2026)
- [Priors learned from legacy reconstructions inherit undetectable overconfidence](https://mlsanity.com/paper/2607.21721/) (2026)

## Abstract (arXiv)

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications, it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g. a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations, and we showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that, starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates.