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This paper introduces an active diffusion-based approach to solve ill-posed inverse problems by training a deep model to map parameter space to observable data. The method iteratively identifies and corrects model misspecifications through posterior uncertainty, enabling it to accurately locate the true parameter region even when initial training data is incomplete. The approach is validated on both a toy problem with infinite solutions and a practical application in Quantum Chromodynamics, demonstrating its robustness and adaptability in challenging scenarios.
Iterative uncertainty correction allows for accurate parameter estimation in inverse problems, even with incomplete prior knowledge.
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.
