{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T05:30:50Z","timestamp":1782970250908,"version":"3.54.5"},"reference-count":76,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"NSF","award":["2111688"],"award-info":[{"award-number":["2111688"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1109\/tac.2025.3631521","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T18:30:57Z","timestamp":1762885857000},"page":"2903-2917","source":"Crossref","is-referenced-by-count":3,"title":["Schr\u00f6dinger Bridge With Quadratic State Cost is Exactly Solvable"],"prefix":"10.1109","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9925-5187","authenticated-orcid":false,"given":"Alexis M. H.","family":"Teter","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, University of California, Santa Cruz, CA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4386-7304","authenticated-orcid":false,"given":"Wenqing","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Iowa State University, Ames, IA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1509-5853","authenticated-orcid":false,"given":"Abhishek","family":"Halder","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, Iowa State University, Ames, IA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BFb0086180","article-title":"Random fields and diffusion processes","volume":"1362","author":"Fllmer","year":"1988","journal-title":"Lect. Notes Math"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2011.11.026"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2457784"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/20M1339982"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3060704"},{"key":"ref6","first-page":"17695","article-title":"Diffusion Schrdinger bridge with applications to score-based generative modeling","volume":"34","author":"Bortoli","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref7","first-page":"10794","article-title":"Deep generative learning via Schrdinger bridge","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Wang","year":"2021"},{"key":"ref8","first-page":"9374","article-title":"Deep generalized Schrdinger bridge","volume":"35","author":"Liu","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-022-10172-5"},{"key":"ref10","first-page":"5802","article-title":"The Schrdinger bridge between Gaussian measures has a closed form","volume-title":"Proc. Int. Conf. Artif. Intell. Statist.","author":"Bunne","year":"2023"},{"key":"ref11","first-page":"62183","article-title":"Diffusion Schrdinger bridge matching","volume":"36","author":"Shi","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref12","first-page":"144","article-title":"ber die umkehrung der naturgesetze","volume":"10","author":"Schrdinger","year":"1931","journal-title":"Sitzungsberichte der Preuss. Phys. Math. Klasse"},{"issue":"4","key":"ref13","first-page":"269","article-title":"Sur la thorie relativiste de l\u2019lectron et l\u2019interprtation de la mcanique quantique","volume":"2","author":"Schrdinger","year":"1932","journal-title":"Annales de l\u2019institut Henri Poincar"},{"key":"ref14","volume-title":"Large Deviations Techniques and Applications","volume":"38","author":"Dembo","year":"2009"},{"issue":"1","key":"ref15","first-page":"11","article-title":"On the probability of large deviations of random magnitudes","volume":"84","author":"Sanov","year":"1957","journal-title":"Matematicheskii Sbornik"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993227"},{"issue":"14","key":"ref17","first-page":"83","article-title":"Rsolution d\u2019un systme d\u2019quations de m. schrdinger","volume":"19","author":"Fortet","year":"1940","journal-title":"J. de Mathmatiques Pures et Appliques"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.2307\/1970151"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532864"},{"key":"ref20","first-page":"61","article-title":"Schrdinger bridges from 1931 to 1991","volume-title":"Proc. 4th Latin Amer. Congr. Probability Math. Statist.","author":"Wakolbinger","year":"1990"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1063\/1.528840"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01222509"},{"key":"ref23","article-title":"Stochastic derivatives and generalized H-transforms of Markov processes","author":"Lonard","year":"2011"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050002"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0803-z"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.5802\/afst.1546"},{"key":"ref27","first-page":"2292","article-title":"Sinkhorn distances: Lightspeed computation of optimal transport","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"26","author":"Cuturi","year":"2013"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-010-9595-1"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2015.7170905"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2018.2791362"},{"key":"ref31","volume-title":"Optimal Control: Linear Quadratic Methods","author":"Anderson","year":"2007"},{"key":"ref32","article-title":"Likelihood training of schrdinger bridge using forward-backward SDEs theory","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Chen","year":"2021"},{"key":"ref33","article-title":"Denoising diffusion bridge models","author":"Zhou","year":"2023"},{"issue":"374","key":"ref34","first-page":"1","article-title":"Diffusion bridge mixture transports, schrdinger bridge problems and generative modeling","volume":"24","author":"Peluchetti","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"ref35","first-page":"75517","article-title":"Entropic neural optimal transport via diffusion processes","volume":"36","author":"Gushchin","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref36","first-page":"18932","article-title":"Building the bridge of Schrdinger: A continuous entropic optimal transport benchmark","volume":"36","author":"Gushchin","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v38i12.29238"},{"key":"ref38","article-title":"Score-based generative modeling through stochastic differential equations","author":"Song","year":"2020"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/cdc51059.2022.9993420"},{"key":"ref40","first-page":"22042","article-title":"I2SB: Image-to-image Schrdinger bridge","volume-title":"Proc. 40th Int. Conf. Mach. Learn.","author":"Liu","year":"2023"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/LCSYS.2023.3326836"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2023.3337588"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.23919\/ACC55779.2023.10156176"},{"key":"ref44","article-title":"Transport meets variational inference: Controlled Monte Carlo diffusions","volume-title":"Proc. 12th Int. Conf. Learn. Representations","author":"Vargas","year":"2024"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.23919\/acc50511.2021.9482813"},{"key":"ref46","article-title":"Reflected Schrdinger bridge for constrained generative modeling","author":"Deng","year":"2024"},{"key":"ref47","volume-title":"Schrdinger Equations and Diffusion Theory","volume":"86","author":"Nagasawa","year":"2012"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.27.1774"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2025.3548396"},{"key":"ref50","volume-title":"Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"1972"},{"key":"ref51","volume-title":"Quantum Field Theory in a Nutshell","volume":"7","author":"Zee","year":"2010"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198834625.001.0001"},{"key":"ref53","volume-title":"The Theory of Matrices","volume":"1","author":"Gantmakher","year":"2000"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1007\/BF01397184"},{"key":"ref56","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-9027-4","volume-title":"Schrdinger Diffusion Processes","author":"Aebi","year":"1996"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1137\/16M1061382"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/BF00247467"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1017\/9781108587280"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1090\/noti936"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1137\/24m1646145"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1866.66.161"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-70845-0"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100022313"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1137\/0503060"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(81)90005-1"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572374"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-018-1667-y"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2019.2958556"},{"key":"ref70","volume-title":"Applied Nonlinear Programming","author":"Himmelblau","year":"2018"},{"key":"ref71","article-title":"Markov kernels, distances and optimal control: A parable of linear quadratic non-Gaussian distribution steering","author":"Teter","year":"2025"},{"key":"ref72","volume-title":"Stochastic Differential Equations: An Introduction With Applications","author":"Oksendal","year":"2013"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-696-4_13"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160030302"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/42889"},{"key":"ref76","volume-title":"Methods of Mathematical Physics","volume":"1","author":"Courant","year":"2008"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/9\/11495383\/11239424-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/9\/11495383\/11239424.pdf?arnumber=11239424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T19:51:01Z","timestamp":1777405861000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11239424\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":76,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tac.2025.3631521","relation":{},"ISSN":["0018-9286","1558-2523","2334-3303"],"issn-type":[{"value":"0018-9286","type":"print"},{"value":"1558-2523","type":"electronic"},{"value":"2334-3303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5]]}}}