{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T04:58:44Z","timestamp":1780635524935,"version":"3.54.1"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032049643","type":"print"},{"value":"9783032049650","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-04965-0_3","type":"book-chapter","created":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T08:05:20Z","timestamp":1758182720000},"page":"25-35","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ambiguous Medical Image Segmentation Using Diffusion Schr\u00f6dinger Bridge"],"prefix":"10.1007","author":[{"given":"Lalith Bharadwaj","family":"Baru","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kamalaker","family":"Dadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tapabrata","family":"Chakraborti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raju S.","family":"Bapi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,19]]},"reference":[{"issue":"2","key":"3_CR1","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.jacr.2003.11.001","volume":"1","author":"HR Alpert","year":"2004","unstructured":"Alpert, H.R., Hillman, B.J.: Quality and variability in diagnostic radiology. J. Am. Coll. Radiol. 1(2), 127\u2013132 (2004)","journal-title":"J. Am. Coll. Radiol."},{"issue":"3","key":"3_CR2","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1016\/0304-4149(82)90051-5","volume":"12","author":"BDO Anderson","year":"1982","unstructured":"Anderson, B.D.O.: Reverse-time diffusion equation models. Stochastic Processes Appli. 12(3), 313\u2013326 (1982)","journal-title":"Stochastic Processes Appli."},{"issue":"3","key":"3_CR3","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1148\/radiol.2323032035","volume":"232","author":"SG Armato","year":"2004","unstructured":"Armato, S.G., et al.: Lung image database consortium: developing a resource for the medical imaging research community. Radiology 232(3), 739\u2013748 (2004)","journal-title":"Radiology"},{"key":"3_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-32245-8_1","volume-title":"Medical Image Computing and Computer Assisted Intervention \u2013 MICCAI 2019","author":"D Yang","year":"2019","unstructured":"Yang, D., et al.: Searching learning strategy with reinforcement learning for 3d medical image segmentation. In: Shen, D., et al. (eds.) MICCAI 2019. LNCS, vol. 11765, pp. 3\u201311. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-32245-8_1"},{"key":"3_CR5","unstructured":"Chang, Z., Koulieris, G.A., Shum, H.P.H.: On the design fundamentals of diffusion models: A survey. arXiv preprint, arXiv:2306.04542 (2023)"},{"key":"3_CR6","unstructured":"Chen, T., Liu, G.-H., Theodorou, E.A.: Likelihood training of schr\u00f6dinger bridge using forward-backward sdes theory. arXiv preprint, arXiv:2110.11291 (2021)"},{"issue":"2","key":"3_CR7","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1137\/20M1339982","volume":"63","author":"Y Chen","year":"2021","unstructured":"Chen, Y., Georgiou, T.T., Pavon, M.: Stochastic control liaisons: richard sinkhorn meets gaspard monge on a schrodinger bridge. SIAM Rev. 63(2), 249\u2013313 (2021)","journal-title":"SIAM Rev."},{"key":"3_CR8","first-page":"8780","volume":"34","author":"P Dhariwal","year":"2021","unstructured":"Dhariwal, P., Nichol, A.: Diffusion models beat gans on image synthesis. Adv. Neural. Inf. Process. Syst. 34, 8780\u20138794 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"1","key":"3_CR9","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1038\/s41746-021-00460-1","volume":"4","author":"D Eng","year":"2021","unstructured":"Eng, D., et al.: Automated coronary calcium scoring using deep learning with multicenter external validation. NPJ Digital Med. 4(1), 88 (2021)","journal-title":"NPJ Digital Med."},{"key":"3_CR10","first-page":"6840","volume":"33","author":"J Ho","year":"2020","unstructured":"Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Adv. Neural. Inf. Process. Syst. 33, 6840\u20136851 (2020)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"3_CR11","unstructured":"Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022)"},{"key":"3_CR12","unstructured":"Kohl, S., et al.: A probabilistic u-net for segmentation of ambiguous images. Adv. Neural Inform. Process. Syst. 31 (2018)"},{"issue":"31","key":"3_CR13","doi-asserted-by":"publisher","first-page":"8777","DOI":"10.1073\/pnas.1601827113","volume":"113","author":"RHJM Kurvers","year":"2016","unstructured":"Kurvers, R.H.J.M.: Boosting medical diagnostics by pooling independent judgments. Proc. Natl. Acad. Sci. 113(31), 8777\u20138782 (2016)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"1","key":"3_CR14","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/18.61115","volume":"37","author":"J Lin","year":"1991","unstructured":"Lin, J.: Divergence measures based on the shannon entropy. IEEE Trans. Inf. Theory 37(1), 145\u2013151 (1991)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3_CR15","unstructured":"Liu, G.-H., Vahdat, A., Huang, D.-A., Theodorou, E.A., Nie, W., Anandkumar, A.: I2sb: Image-to-image schr\u00f6dinger bridge. arXiv preprint, arXiv:2302.05872 (2023)"},{"key":"3_CR16","doi-asserted-by":"publisher","unstructured":"Pavon, M., Wakolbinger, A.: On free energy, stochastic control, and schr\u00f6dinger processes. In: Di Masi, G.B., Gombani, A., Kurzhansky, A.B. (eds,) Modeling, Estimation and Control of Systems with Uncertainty. Progress in Systems and Control Theory, vol 10. Birkh\u00e4user, Boston, MA (1991). https:\/\/doi.org\/10.1007\/978-1-4612-0443-5_22","DOI":"10.1007\/978-1-4612-0443-5_22"},{"key":"3_CR17","doi-asserted-by":"crossref","unstructured":"Rahman, A., Valanarasu, J.M.J., Hacihaliloglu, I., Patel, V.M.: Ambiguous medical image segmentation using diffusion models. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 11536\u201311546 (2023)","DOI":"10.1109\/CVPR52729.2023.01110"},{"key":"3_CR18","doi-asserted-by":"crossref","unstructured":"Risken, H., Risken, H.: Fokker-planck equation. Springer (1996)","DOI":"10.1007\/978-3-642-61544-3"},{"key":"3_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/978-3-319-24574-4_28","volume-title":"Medical Image Computing and Computer-Assisted Intervention \u2013 MICCAI 2015","author":"O Ronneberger","year":"2015","unstructured":"Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234\u2013241. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-24574-4_28"},{"key":"3_CR20","doi-asserted-by":"crossref","unstructured":"Saharia, C., et\u00a0al.: Palette: Image-to-image diffusion models, pp. 1\u201310 (2022)","DOI":"10.1145\/3528233.3530757"},{"key":"3_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/978-3-030-59861-7_9","volume-title":"Machine Learning in Medical Imaging","author":"R Selvan","year":"2020","unstructured":"Selvan, R., Faye, F., Middleton, J., Pai, A.: Uncertainty quantification in medical image segmentation with normalizing flows. In: Liu, M., Yan, P., Lian, C., Cao, X. (eds.) MLMI 2020. LNCS, vol. 12436, pp. 80\u201390. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-59861-7_9"},{"key":"3_CR22","unstructured":"Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. arXiv preprint, arXiv:2011.13456 (2020)"},{"issue":"8","key":"3_CR23","doi-asserted-by":"publisher","first-page":"1249","DOI":"10.1016\/j.jspi.2013.03.018","volume":"143","author":"GJ Sz\u00e9kely","year":"2013","unstructured":"Sz\u00e9kely, G.J., Rizzo, M.L.: Energy statistics: a class of statistics based on distances. J. Statistical Planning Inference 143(8), 1249\u20131272 (2013)","journal-title":"J. Statistical Planning Inference"},{"issue":"9","key":"3_CR24","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.3390\/e23091134","volume":"23","author":"F Vargas","year":"2021","unstructured":"Vargas, F., Thodoroff, P., Lamacraft, A., Lawrence, N.: Solving schr\u00f6dinger bridges via maximum likelihood. Entropy 23(9), 1134 (2021)","journal-title":"Entropy"},{"issue":"7","key":"3_CR25","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1162\/NECO_a_00142","volume":"23","author":"P Vincent","year":"2011","unstructured":"Vincent, P.: A connection between score matching and denoising autoencoders. Neural Comput. 23(7), 1661\u20131674 (2011)","journal-title":"Neural Comput."},{"key":"3_CR26","doi-asserted-by":"crossref","unstructured":"Zbinden, L., et al.: Stochastic segmentation with conditional categorical diffusion models. In: ICCV, pp. 1119\u20131129 (2023)","DOI":"10.1109\/ICCV51070.2023.00109"}],"container-title":["Lecture Notes in Computer Science","Medical Image Computing and Computer Assisted Intervention \u2013 MICCAI 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-04965-0_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T22:04:37Z","timestamp":1758233077000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-04965-0_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,19]]},"ISBN":["9783032049643","9783032049650"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-04965-0_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,19]]},"assertion":[{"value":"19 September 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors declare that they have no financial or non-financial competing interests that could have influenced the work reported in this paper.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"MICCAI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Medical Image Computing and Computer-Assisted Intervention","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Daejeon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Korea (Republic of)","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"miccai2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conferences.miccai.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}