A Bayesian Revolution in the Age of Deep Learning
M. Zach, M. Unser, L. Glaszner, A. Habring, M. Kuric, T. Pock, F. Knoll, E. Kobler
Proceedings of the Twelfth Conference on Applied Inverse Problems (AIP'25), Rio de Janeiro, Federative Republic of Brazil, July 28-August 1, 2025, pp. 138.
Many inverse-problem solvers still chase a single minimiser of a learned objective. However, the single minimizer can be misleading when there are modelling errors, data gaps, or out-of-distribution conditions. Treating modern generative networks as probabilistic priors replaces point estimation with posterior sampling, yielding the entire family of solutions consistent with data and physics. Posterior sampling needs two ingredients: expressive priors that can be learned from data, and scalable algorithms that navigate the resulting high-dimensional, non-convex landscapes. In this talk, we cover recent approaches to these problems. Specifically, we show how the modeling can be addressed by deep neural networks and more classical fields-of-experts models. For both, we show how recent advances in nonsmooth and nonconvex sampling enable the efficient learning of the prior as well as the sampling of the posterior by combining ideas from diffusion models, nonsmooth Langevin sampling, and latent variable models. Finally, we discuss how the adaptation of the model size can be a potential avenue to good generalization when there is little data available. Recasting reconstruction as stochastic exploration, not deterministic optimisation, thus opens a clearer, more reliable path for inverse problems in the deep-learning era: A Bayesian revolution.
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AUTHOR="Zach, M. and Unser, M. and Glaszner, L. and Habring, A. and
Kuric, M. and Pock, T. and Knoll, F. and Kobler, E.",
TITLE="A {B}ayesian Revolution in the Age of Deep Learning",
BOOKTITLE="Proceedings of the Twelfth Conference on Applied Inverse
Problems ({AIP'25})",
YEAR="2025",
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pages="138",
address="Rio de Janeiro, Federative Republic of Brazil",
month="July 28-August 1,",
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