{"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/conditional-score-based-diffusion-models-for-2","title":"Conditional score-based diffusion models for Bayesian inference in infinite dimensions","arxiv_id":"2305.19147","date":"2023-05-28","proceeding":"NeurIPS 2023 11","authors":["Lorenzo Baldassari","Ali Siahkoohi","Josselin Garnier","Knut Solna","Maarten V. de Hoop"],"abstract":"Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the posterior distribution. However, using SDMs for inverse problems in infinite-dimensional function spaces has only been addressed recently, primarily through methods that learn the unconditional score. While this approach is advantageous for some inverse problems, it is mostly heuristic and involves numerous computationally costly forward operator evaluations during posterior sampling. To address these limitations, we propose a theoretically grounded method for sampling from the posterior of infinite-dimensional Bayesian linear inverse problems based on amortized conditional SDMs. In particular, we prove that one of the most successful approaches for estimating the conditional score in finite dimensions - the conditional denoising estimator - can also be applied in infinite dimensions. A significant part of our analysis is dedicated to demonstrating that extending infinite-dimensional SDMs to the conditional setting requires careful consideration, as the conditional score typically blows up for small times, contrarily to the unconditional score. We conclude by presenting stylized and large-scale numerical examples that validate our approach, offer additional insights, and demonstrate that our method enables large-scale, discretization-invariant Bayesian inference.","url_abs":"https://arxiv.org/abs/2305.19147v2","url_pdf":"https://arxiv.org/pdf/2305.19147v2.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":"conditional-score-based-diffusion-models-for-2","repo_url":"https://github.com/alisiahkoohi/csgm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"denoising","task_name":"Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2305.19147","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.19147"}},"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/alisiahkoohi/csgm","reach":null}],"summary":{"ran":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"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":"b4537186753cc754","entry":"FourierNeuralLayer1D","repo":"alisiahkoohi/csgm","repo_kind":"official","path":"csgm/network_conditional.py","file_url":"https://github.com/alisiahkoohi/csgm/blob/HEAD/csgm/network_conditional.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b4537186753cc754"}},{"code_sha256_prefix":"778cdb06a02005ac","entry":"ConditionalScoreModel1D","repo":"alisiahkoohi/csgm","repo_kind":"official","path":"csgm/network_conditional.py","file_url":"https://github.com/alisiahkoohi/csgm/blob/HEAD/csgm/network_conditional.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"778cdb06a02005ac"}},{"code_sha256_prefix":"af8861c727b86643","entry":"FourierNeuralOperator1D","repo":"alisiahkoohi/csgm","repo_kind":"official","path":"csgm/network_conditional.py","file_url":"https://github.com/alisiahkoohi/csgm/blob/HEAD/csgm/network_conditional.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"af8861c727b86643"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}