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Proximal Residual Flows for Bayesian Inverse Problems

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Scale Space and Variational Methods in Computer Vision (SSVM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14009))

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Abstract

Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows. Based on the fact, that proximal neural networks are by definition averaged operators, we ensure invertibility of certain residual blocks. Moreover, we extend the architecture to conditional proximal residual flows for posterior reconstruction within Bayesian inverse problems. We demonstrate the performance of proximal residual flows on numerical examples.

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Notes

  1. 1.

    https://github.com/johertrich/Proximal_Residual_Flows.

  2. 2.

    For the data generation and evaluation of this example, we use the code of [44] available at https://github.com/noegroup/stochastic_normalizing_flows.

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Acknowledgements

Funding by the German Research Foundation (DFG) within the project STE 571/16-1 is gratefully acknowledged.

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Authors and Affiliations

  1. Institute of Mathematics, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Johannes Hertrich

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  1. Johannes Hertrich
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Correspondence to Johannes Hertrich .

Editor information

Editors and Affiliations

  1. CNRS, Université Côte d'Azur, Sophia-Antipolis, France

    Luca Calatroni

  2. University of Insubria, Como, Italy

    Marco Donatelli

  3. University of Bologna, Bologna, Italy

    Serena Morigi

  4. University of Modena and Reggio Emilia, Modena, Italy

    Marco Prato

  5. University of Genova, Genova, Italy

    Matteo Santacesaria

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Hertrich, J. (2023). Proximal Residual Flows for Bayesian Inverse Problems. In: Calatroni, L., Donatelli, M., Morigi, S., Prato, M., Santacesaria, M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2023. Lecture Notes in Computer Science, vol 14009. Springer, Cham. https://doi.org/10.1007/978-3-031-31975-4_16

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  • DOI: https://doi.org/10.1007/978-3-031-31975-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-31974-7

  • Online ISBN: 978-3-031-31975-4

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