eprintid: 10194632 rev_number: 6 eprint_status: archive userid: 699 dir: disk0/10/19/46/32 datestamp: 2024-07-16 07:57:28 lastmod: 2024-07-16 07:57:28 status_changed: 2024-07-16 07:57:28 type: proceedings_section metadata_visibility: show sword_depositor: 699 creators_name: Hagemann, Paul creators_name: Hertrich, Johannes creators_name: Altekrüger, Fabian creators_name: Beinert, Robert creators_name: Chemseddine, Jannis creators_name: Steidl, Gabriele title: Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel ispublished: pub divisions: UCL divisions: B04 divisions: F48 keywords: Bayesian inverse Problems, MMD, Gradient Flows, Deep Learning note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modelling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings. date: 2024-04-08 date_type: published publisher: ICLR official_url: https://openreview.net/forum?id=YrXHEb2qMb oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2297228 lyricists_name: Hertrich, Johannes lyricists_id: JHERT98 actors_name: Hertrich, Johannes actors_id: JHERT98 actors_role: owner full_text_status: public pres_type: paper series: International Conference on Learning Representations place_of_pub: Vienna, Austria event_title: The Twelfth International Conference on Learning Representations event_location: Vienna event_dates: 7 Jan 2024 - 11 Jul 2024 book_title: Proceedings of the Twelfth International Conference on Learning Representations : ICLR 2024 citation: Hagemann, Paul; Hertrich, Johannes; Altekrüger, Fabian; Beinert, Robert; Chemseddine, Jannis; Steidl, Gabriele; (2024) Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel. In: Proceedings of the Twelfth International Conference on Learning Representations : ICLR 2024. ICLR: Vienna, Austria. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10194632/1/posterior.pdf