{"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/q-malizing-flow-and-infinitesimal-density","title":"Computing high-dimensional optimal transport by flow neural networks","arxiv_id":"2305.11857","date":"2023-05-19","proceeding":null,"authors":["Chen Xu","Xiuyuan Cheng","Yao Xie"],"abstract":"Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.","url_abs":"https://arxiv.org/abs/2305.11857v5","url_pdf":"https://arxiv.org/pdf/2305.11857v5.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":"q-malizing-flow-and-infinitesimal-density","repo_url":"https://github.com/hamrel-cxu/flowot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"density-ratio-estimation","task_name":"Density Ratio Estimation"},{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"},{"task_slug":"image-to-image-translation","task_name":"Image-to-Image Translation"},{"task_slug":"mutual-information-estimation","task_name":"Mutual Information Estimation"}],"methods":[{"method_slug":"normalizing-flows","method_name":"Normalizing Flows"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2305.11857","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}