{"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/simulating-infinite-dimensional-nonlinear","title":"Infinite-dimensional Diffusion Bridge Simulation via Operator Learning","arxiv_id":"2405.18353","date":"2024-05-28","proceeding":null,"authors":["Gefan Yang","Elizabeth Louise Baker","Michael L. Severinsen","Christy Anna Hipsley","Stefan Sommer"],"abstract":"The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling natural data can be challenging due to both the intractability of the drift term and continuous representations of the data. Although several methods are available to simulate finite-dimensional diffusion bridges, infinite-dimensional cases remain under explored. This paper presents a method that merges score matching techniques with operator learning, enabling a direct approach to learn the infinite-dimensional bridge and achieving a discretization equivariant bridge simulation. We conduct a series of experiments, ranging from synthetic examples with closed-form solutions to the stochastic nonlinear evolution of real-world biological shape data. Our method demonstrates high efficacy, particularly due to its ability to adapt to any resolution without extra training.","url_abs":"https://arxiv.org/abs/2405.18353v3","url_pdf":"https://arxiv.org/pdf/2405.18353v3.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":"simulating-infinite-dimensional-nonlinear","repo_url":"https://github.com/bookdiver/scoreoperator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"operator-learning","task_name":"Operator learning"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2405.18353","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}