Generalization and Guarantees in Deep Learning for Inverse Problems

Characterize the generalization behavior of deep learning-based methods for inverse problems across diverse datasets and ascertain the trade-off between empirical performance and robust theoretical guarantees such as stability, robustness, and convergence.

Background

The authors emphasize a paradigm shift toward data-driven approaches that often outperform handcrafted priors. However, this comes with interpretability challenges and the need for rigorous guarantees, especially in safety-critical domains.

They explicitly note that generalization across datasets and balancing empirical performance against theoretical assurances remain unresolved, motivating structured learning and new theory tailored to deep learning in inverse problems.

References

Open questions remain regarding the generalization of these models across diverse datasets and the crucial balance between empirical performance and robust theoretical guarantees.

— Data-driven approaches to inverse problems  (2506.11732 - Schönlieb et al., 13 Jun 2025) in Section "The Data Driven - Knowledge Informed Paradigm", Chapter "Perspectives"

It clarifies what deep learning and modern AI can achieve through representation learning, increased capacity, wider contextual modelling, optimization, and large empirical priors, while identifying fundamental problems that remain unresolved, including limits imposed by acquisition, sampling, non-identifiability, decision objectives, and dependence on the training distribution.

— Rethinking Image Processing for the Age of AI: A Problem-First Framework for Scientific Progress  (2608.26833 - Qiu, 27 Aug 2026) in Introduction, second contribution

Despite these results, LUD-DIF has two main limitations. First, it requires a known or approximate forward operator, limiting its use in blind inverse problems and semantic modality translation. Second, although we bound the error introduced by the weak-coupling assumption, how to reduce this error remains open. Future work may investigate transformed or latent representations, such as wavelet spaces and neural-network embeddings, to tighten the bound, together with efficient sampling and model distillation to improve scalability.

— Diffusion Based Unpaired Data Learning for Inverse Problems  (2609.01370 - Bao et al., 1 Sep 2026) in Section 5, Conclusion and Future Work