用主动扩散模型解决先验不全时的反问题，自动找对参数范围。
Active Diffusion-Based Inference for Ill-Posed Inverse Problems under Incomplete Priors
- 通过后验不确定性迭代检测模型偏差，自适应扩展参数空间。
- 在初始范围不含真值时仍能收敛到正确解，适用于无限多解的反问题。
- 适合科学计算中先验信息不足的场景，如量子强子物理参数反演。
许多科学与工程应用需从可观测数据中估计未知参数——这类反问题因非线性、噪声和病态性而极具挑战。本文提出一种基于主动扩散模型的反问题求解方法：训练扩散模型学习参数空间与可观测空间间的映射；通过迭代检测并修正模型误设，利用后验不确定性发现并学习正确的参数区域，即使初始训练范围不包含真实参数也能成功。该方法为自适应域扩充提供了贝叶斯理论依据，确保在先验知识不全时仍具鲁棒性。我们在一个具有无穷多解的模拟反问题，以及强子物理中核子结构分析里量子关联函数到事件可观测量的参数化任务上验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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