Nonlinear Inverse Problems with Deep Generative Models
A special issue of Axioms (ISSN 2075-1680).
Deadline for manuscript submissions: 30 June 2026 | Viewed by 200
Special Issue Editor
Special Issue Information
Dear Colleagues,
Deep generative models, such as diffusion models, generative adversarial networks (GANs), and variational autoencoders (VAEs), have revolutionized the field of nonlinear inverse problems. These models provide powerful, data-driven priors that can effectively regularize ill-posed problems, enabling high-quality reconstruction and uncertainty quantification in scenarios where traditional methods fail. They have demonstrated remarkable success in applications ranging from computational imaging and medical tomography to seismic inversion and remote sensing.
(a) This Special Issue will focus on the theoretical foundations, novel algorithmic development, and practical applications of deep generative models for solving nonlinear inverse problems.(b) We invite contributions that explore topics including, but not limited to, the following:
- Theoretical guarantees for recovery and convergence in nonlinear settings.
- Robustness, generalization, and uncertainty quantification for generative priors.
- Efficient sampling and training strategies for high-dimensional problems.
- Integration of physical models and domain knowledge with deep generative networks.
- Applications in computational photography, medical imaging, geophysics, and non-Euclidean domains.
- The intersection of large-scale generative models (e.g., large language and diffusion models) with inverse problem solving.
(c) Purpose: The purpose of this Special Issue is to consolidate the latest advancements, address open challenges, and chart future directions at the intersection of deep generative modeling and nonlinear inverse problems. It aims to provide a platform for researchers to present innovative methodologies that push the boundaries of what is possible in reconstructing complex, real-world signals from incomplete or corrupted measurements.
This Special Issue will supplement the existing literature by moving beyond linear inverse problems and shallow priors to concentrate on the unique challenges and opportunities presented by nonlinear forward models and deep, high-dimensional generative priors. While the existing literature has established the promise of deep learning for inversion, this issue will specifically highlight how advanced generative models provide a coherent framework for handling multimodality, learning complex data manifolds, and solving previously intractable nonlinear problems. It will illuminate the pathway from empirical success to principled, theoretically grounded solutions.
Prof. Dr. Zhaoqiang Liu
Guest Editor
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Keywords
- deep generative models
- nonlinear inverse problems
- diffusion models
- Ill-posed problems
- Bayesian reconstruction
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