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Recently, methods such as Gaussian process regression (GPR) and conditional diffusion models have shown advanced performance in SSF forecasting. However, limitations remain: standard GPR fails to capture the range-depth spatial correlations, and conditional diffusion models struggle with continuous forecasting. To address these issues, we integrate multi-output GPR and conditional diffusion models to enable continuous forecasting of range-dependent SSFs, employing careful designs for diffusion noise, neural architecture, and training strategies. Our experiments, conducted on HYCOM hindcast datasets from the South China Sea, demonstrate that our proposed model outperforms state-of-the-art baselines in forecasting range-dependent SSFs at any given time and the associated underwater transmission losses.<\/jats:p>","DOI":"10.1121\/10.0043819","type":"journal-article","created":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T12:39:39Z","timestamp":1778848779000},"page":"4204-4222","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Continuous forecasting of range-dependent ocean sound speed field: Diffusion model meets multi-output Gaussian process"],"prefix":"10.1121","volume":"159","author":[{"given":"Ce","family":"Gao","sequence":"first","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou, 310027,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyuan","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou, 310027,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0097-0547","authenticated-orcid":false,"given":"Lei","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou, 310027,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9440-3219","authenticated-orcid":false,"given":"Ting","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou, 310027,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8205-9334","authenticated-orcid":false,"given":"Jianlong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University 1 , Hangzhou, 310027,","place":["China"]},{"name":"Hainan Institute, Zhejiang University 2 , 572025, Sanya,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0471-062X","authenticated-orcid":false,"given":"Peter","family":"Gerstoft","sequence":"additional","affiliation":[{"name":"Technical University of Denmark 3 , 2800 Lyngby,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"231","published-online":{"date-parts":[[2026,5,15]]},"reference":[{"key":"2026051508393181300_c1","volume-title":"Computational Ocean Acoustics","year":"2011"},{"issue":"6","key":"2026051508393181300_c2","doi-asserted-by":"publisher","first-page":"064801","DOI":"10.1121\/10.0005069","article-title":"Matched field source localization with Gaussian processes","volume":"1","year":"2021","journal-title":"JASA Express Lett."},{"issue":"8","key":"2026051508393181300_c3","doi-asserted-by":"publisher","first-page":"084801","DOI":"10.1121\/10.0013365","article-title":"Seabed classification and source localization with Gaussian processes and machine learning","volume":"2","year":"2022","journal-title":"JASA Express Lett."},{"issue":"1","key":"2026051508393181300_c4","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1109\/JOE.2014.2307194","article-title":"A two-stage approach for the estimation of doubly spread acoustic channels","volume":"40","year":"2015","journal-title":"IEEE J. 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