Active Diffusion-Based Inference for Ill-Posed Inverse Problems under Incomplete Priors

2026-08-27

AI Summary

本文提出了一种基于主动扩散的逆问题求解方法，通过训练映射模型并迭代修正不确定性来解决在先验知识不完整情况下的非线性、噪声和不适定性问题。

Abstract

Many scientific and engineering applications require estimating unknown parameters from experimentally observable data -- an inverse problem that is inherently challenging due to nonlinearity, noise, and ill-posedness. In this paper, we propose an active diffusion-based inverse problem solver. A DM is trained to learn the mapping between the parameter space and the observable space. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method discovers and learns the correct region of parameter space, even when initial training bounds exclude the true parameters. This provides a principled, Bayesian justification for adaptive domain augmentation and ensures robust inference for inverse problems under incomplete prior knowledge. We demonstrate the effectiveness of our inverse solver for a toy inverse problem with infinite solutions, and for the parameterization of the quantum correlation functions to event observables in a Quantum Chromodynamics analysis of nucleon structure.

Problem

• inverse problem
• ill-posedness
• incomplete priors

Innovation

• active diffusion-based inference
• posterior uncertainty
• adaptive domain augmentation
• ill-posed inverse problems
• incomplete priors