{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/posterior-sampling-based-on-gradient-flows-of","title":"Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel","arxiv_id":"2310.03054","date":"2023-10-04","proceeding":null,"authors":["Paul Hagemann","Johannes Hertrich","Fabian Altekrüger","Robert Beinert","Jannis Chemseddine","Gabriele Steidl"],"abstract":"We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. 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.","url_abs":"https://arxiv.org/abs/2310.03054v3","url_pdf":"https://arxiv.org/pdf/2310.03054v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"posterior-sampling-based-on-gradient-flows-of","repo_url":"https://github.com/fabianaltekrueger/conditional_mmd_flows","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"conditional-image-generation","task_name":"Conditional Image Generation"},{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[{"method_slug":"pixel-prediction","method_name":"Inpainting"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2310.03054","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.03054"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/fabianaltekrueger/conditional_mmd_flows","reach":null}],"summary":{"ran_fixture":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"e4ddb1c19a67a3b4","entry":"MMD_derivative_1d","repo":"fabianaltekrueger/conditional_mmd_flows","repo_kind":"official","path":"utils.py","file_url":"https://github.com/fabianaltekrueger/conditional_mmd_flows/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e4ddb1c19a67a3b4"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}