{"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/diffusion-generative-models-in-infinite","title":"Diffusion Generative Models in Infinite Dimensions","arxiv_id":"2212.00886","date":"2022-12-01","proceeding":null,"authors":["Gavin Kerrigan","Justin Ley","Padhraic Smyth"],"abstract":"Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the discretized data, and there are no semantics in the modeling process that relate the observed data to the underlying functional forms. We generalize diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces. A significant benefit of our function space point of view is that it allows us to explicitly specify the space of functions we are working in, leading us to develop methods for diffusion generative modeling in Sobolev spaces. Our approach allows us to perform both unconditional and conditional generation of function-valued data. We demonstrate our methods on several synthetic and real-world benchmarks.","url_abs":"https://arxiv.org/abs/2212.00886v2","url_pdf":"https://arxiv.org/pdf/2212.00886v2.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":"diffusion-generative-models-in-infinite","repo_url":"https://github.com/gavinkerrigan/functional_diffusion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2212.00886","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2212.00886"}},"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/gavinkerrigan/functional_diffusion","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":5},"by_repo_kind":{"official":{"samples":5,"ran":0,"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":"1dbb4026148bf934","entry":"animate","repo":"gavinkerrigan/functional_diffusion","repo_kind":"official","path":"util/visual.py","file_url":"https://github.com/gavinkerrigan/functional_diffusion/blob/HEAD/util/visual.py","link_basis":"harvester_set","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":"1dbb4026148bf934"}},{"code_sha256_prefix":"77054afec0115182","entry":"fwd_process_diagnostic","repo":"gavinkerrigan/functional_diffusion","repo_kind":"official","path":"util/tools.py","file_url":"https://github.com/gavinkerrigan/functional_diffusion/blob/HEAD/util/tools.py","link_basis":"harvester_set","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":"77054afec0115182"}},{"code_sha256_prefix":"18610805ede67b0a","entry":"gaussian_2_wasserstein","repo":"gavinkerrigan/functional_diffusion","repo_kind":"official","path":"util/tools.py","file_url":"https://github.com/gavinkerrigan/functional_diffusion/blob/HEAD/util/tools.py","link_basis":"harvester_set","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":"18610805ede67b0a"}},{"code_sha256_prefix":"b29d4310b4d6ee1f","entry":"gaussian_kl","repo":"gavinkerrigan/functional_diffusion","repo_kind":"official","path":"util/tools.py","file_url":"https://github.com/gavinkerrigan/functional_diffusion/blob/HEAD/util/tools.py","link_basis":"harvester_set","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":"b29d4310b4d6ee1f"}},{"code_sha256_prefix":"f4da87ffd8d1b083","entry":"sobolev_inner_product","repo":"gavinkerrigan/functional_diffusion","repo_kind":"official","path":"diffusion/loss.py","file_url":"https://github.com/gavinkerrigan/functional_diffusion/blob/HEAD/diffusion/loss.py","link_basis":"harvester_set","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":"f4da87ffd8d1b083"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}