Proceedings

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

Jitao Xu, Nobuo Sato, Yaohang Li

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Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence. Main Track. Pages 5119-5127.

https://doi.org/10.24963/ijcai.2026/570

Keywords

  • Machine Learning: Active learning
  • Machine Learning: Generative models
  • Machine Learning: Bayesian learning
  • Multidisciplinary Topics and Applications: Physical sciences

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 diffusion model 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.

Jitao Xu, Nobuo Sato, and Yaohang Li. 2026. Active Diffusion-Based Inference for Ill-Posed Inverse Problems Under Incomplete Priors. In Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence, IJCAI-26. IJCAI, 5119–5127. https://doi.org/10.24963/ijcai.2026/570
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