{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:47:23Z","timestamp":1778604443109,"version":"3.51.4"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Mach Intell"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socioeconomic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high spatial resolution. Recent machine learning approaches have shown promising results in downscaling ESM simulations, outperforming state-of-the-art statistical approaches. However, existing methods require computationally costly retraining for each ESM and extrapolate poorly to climates unseen during training. We address these shortcomings by learning a consistency model that efficiently and accurately downscales arbitrary ESM simulations without retraining in a zero-shot manner. Our approach yields probabilistic downscaled fields at a resolution only limited by the observational reference data. We show that the consistency model outperforms state-of-the-art diffusion models at a fraction of the computational cost and maintains high controllability on the downscaling task. Further, our method generalizes to climate states unseen during training without explicitly formulated physical constraints.<\/jats:p>","DOI":"10.1038\/s42256-025-00980-5","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T10:02:50Z","timestamp":1741860170000},"page":"363-373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Fast, scale-adaptive and uncertainty-aware downscaling of Earth system model fields with generative machine learning"],"prefix":"10.1038","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7097-2161","authenticated-orcid":false,"given":"Philipp","family":"Hess","sequence":"first","affiliation":[]},{"given":"Michael","family":"Aich","sequence":"additional","affiliation":[]},{"given":"Baoxiang","family":"Pan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1239-9034","authenticated-orcid":false,"given":"Niklas","family":"Boers","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"980_CR1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1038\/s41586-021-04283-8","volume":"601","author":"M Kotz","year":"2022","unstructured":"Kotz, M., Levermann, A. & Wenz, L. The effect of rainfall changes on economic production. Nature 601, 223\u2013227 (2022).","journal-title":"Nature"},{"key":"980_CR2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1038\/nclimate3190","volume":"7","author":"T Schneider","year":"2017","unstructured":"Schneider, T. et al. Climate goals and computing the future of clouds. Nat. Clim. Change 7, 3\u20135 (2017).","journal-title":"Nat. Clim. Change"},{"key":"980_CR3","unstructured":"Dinh, L., Krueger, D. & Bengio, Y. NICE: Non-linear Independent Components Estimation. Preprint at http:\/\/arxiv.org\/abs\/1410.8516 (2015)."},{"key":"980_CR4","unstructured":"Goodfellow, I. et al. Generative adversarial nets. In Advances in Neural Information Processing Systems (eds Ghahramani, Z. et al) 2672\u20132680 (MIT, 2014)."},{"key":"980_CR5","doi-asserted-by":"crossref","unstructured":"Groenke, B., Madaus, L. & Monteleoni, C. ClimAlign: unsupervised statistical downscaling of climate variables via normalizing flows. In Proc. 10th International Conference on Climate Informatics 60\u201366 (Association for Computing Machinery, 2020).","DOI":"10.1145\/3429309.3429318"},{"key":"980_CR6","doi-asserted-by":"crossref","first-page":"e2021MS002509","DOI":"10.1029\/2021MS002509","volume":"13","author":"B Pan","year":"2021","unstructured":"Pan, B. et al. Learning to correct climate projection biases. J. Adv. Model. Earth Syst. 13, e2021MS002509 (2021).","journal-title":"J. Adv. Model. Earth Syst."},{"key":"980_CR7","doi-asserted-by":"crossref","unstructured":"Fran\u00e7ois, B., Thao, S. & Vrac, M. Adjusting spatial dependence of climate model outputs with cycle-consistent adversarial networks. Clim. Dyn. 57, 3323\u20133353 (2021).","DOI":"10.1007\/s00382-021-05869-8"},{"key":"980_CR8","doi-asserted-by":"crossref","unstructured":"Harris, L., McRae, A. T. T., Chantry, M., Dueben, P. D. & Palmer, T. N. A generative deep learning approach to stochastic downscaling of precipitation forecasts. J. Adv. Model. Earth Syst. 14, e2022MS003120 (2022).","DOI":"10.1029\/2022MS003120"},{"key":"980_CR9","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1038\/s42256-022-00540-1","volume":"4","author":"P Hess","year":"2022","unstructured":"Hess, P., Dr\u00fcke, M., Petri, S., Strnad, F. M. & Boers, N. Physically constrained generative adversarial networks for improving precipitation fields from Earth system models. Nat. Mach. Intell. 4, 828\u2013839 (2022).","journal-title":"Nat. Mach. Intell."},{"key":"980_CR10","doi-asserted-by":"crossref","first-page":"e2023EF004002","DOI":"10.1029\/2023EF004002","volume":"11","author":"P Hess","year":"2023","unstructured":"Hess, P., Lange, S., Sch\u00f6tz, C. & Boers, N. Deep learning for bias-correcting CMIP6-class Earth system models. Earth\u2019s Future 11, e2023EF004002 (2023).","journal-title":"Earth\u2019s Future"},{"key":"980_CR11","unstructured":"M. Arjovsky. & L. Bottou. Towards principled methods for training generative adversarial networks. In 5th International Conference on Learning Representations (OpenReview.net, 2017)."},{"key":"980_CR12","unstructured":"Dhariwal, P. & Nichol, A. Diffusion models beat GANs on image synthesis. In Advances in Neural Information Processing Systems (eds Ranzato, M. et al.) 8780\u20138794 (Curran Associates, 2021)."},{"key":"980_CR13","unstructured":"Song, Y. et al. Score-based generative modeling through stochastic differential equations. In 9th International Conference on Learning Representations 8780\u20138794 (Curran Associates, 2021)."},{"key":"980_CR14","unstructured":"Clark, K. & Jaini, P. Text-to-image diffusion models are zero shot classifiers. In Advances in Neural Information Processing Systems (eds Oh, T. et al.) 58921\u201358937 (Curran Associates, 2023)."},{"key":"980_CR15","doi-asserted-by":"crossref","unstructured":"Sauer, A., Lorenz, D., Blattmann, A. & Rombach, R. Adversarial diffusion distillation. In Computer Vision\u2014ECCV 2024 87\u2013103 (Springer Nature, 2024).","DOI":"10.1007\/978-3-031-73016-0_6"},{"key":"980_CR16","unstructured":"Meng, C. et al. SDEdit: guided image synthesis and editing with stochastic differential equations. In 10th International Conference on Learning Representations (Curran Associates, 2022)."},{"key":"980_CR17","doi-asserted-by":"crossref","unstructured":"Bischoff, T. & Deck, K. Unpaired downscaling of fluid flows with diffusion bridges. Artific. Intell. Earth Syst. 3, e230039 (2024).","DOI":"10.1175\/AIES-D-23-0039.1"},{"key":"980_CR18","unstructured":"Wan, Z. Y. et al. Debias coarsely, sample conditionally: statistical downscaling through optimal transport and probabilistic diffusion models. In Advances in Neural Information Processing Systems (eds Oh, A. et al.) 47749\u201347763 (NeurIPS, 2023)."},{"key":"980_CR19","unstructured":"Karras, T., Aittala, M., Aila, T. & Laine, S. Elucidating the design space of diffusion-based generative models. In Advances in Neural Information Processing Systems (eds Koyejo, S. et al.) 26565\u201326577 (NeurIPS, 2022)."},{"key":"980_CR20","unstructured":"Esser, P. et al. Scaling rectified flow transformers for high-resolution image synthesis. In Proc. of the 41st International Conference on Machine Learning (eds Salakhutdinov, R. et al.) 12606\u201312633 (JMLR.org, 2024)."},{"key":"980_CR21","unstructured":"Luhman, E. & Luhman, T. Knowledge distillation in iterative generative models for improved sampling speed. Preprint at http:\/\/arxiv.org\/abs\/2101.02388 (2021)."},{"key":"980_CR22","unstructured":"Zheng, H., Nie, W., Vahdat, A. & Anandkumar, A. Fast Training of Diffusion Models with Masked Transformers. In Transactions on Machine Learning Research (OpenReview.net, 2024)."},{"key":"980_CR23","unstructured":"Song, Y., Dhariwal, P., Chen, M. & Sutskever, I. Consistency models. In Proc. 40th International Conference on Machine Learning (eds Krause, A. et al.) 32211\u201332252 (PMLR, 2023)."},{"key":"980_CR24","first-page":"1","volume":"24","author":"P Harder","year":"2023","unstructured":"Harder, P. et al. Hard-constrained deep learning for climate downscaling. J. Mach. Learn. Res. 24, 1\u201340 (2023).","journal-title":"J. Mach. Learn. Res."},{"key":"980_CR25","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1038\/s41586-021-03854-z","volume":"597","author":"S Ravuri","year":"2021","unstructured":"Ravuri, S. et al. Skilful precipitation nowcasting using deep generative models of radar. Nature 597, 672\u2013677 (2021).","journal-title":"Nature"},{"key":"980_CR26","doi-asserted-by":"crossref","first-page":"e2020GL087232","DOI":"10.1029\/2020GL087232","volume":"47","author":"B Tian","year":"2020","unstructured":"Tian, B. & Dong, X. The double-ITCZ bias in CMIP3, CMIP5, and CMIP6 models based on annual mean precipitation. Geophys. Res. Lett. 47, e2020GL087232 (2020).","journal-title":"Geophys. Res. Lett."},{"key":"980_CR27","doi-asserted-by":"crossref","first-page":"6938","DOI":"10.1175\/JCLI-D-14-00754.1","volume":"28","author":"AJ Cannon","year":"2015","unstructured":"Cannon, A. J., Sobie, S. R. & Murdock, T. Q. Bias correction of GCM precipitation by quantile mapping: how well do methods preserve changes in quantiles and extremes? J. Clim. 28, 6938\u20136959 (2015).","journal-title":"J. Clim."},{"key":"980_CR28","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1175\/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2","volume":"15","author":"H Hersbach","year":"2000","unstructured":"Hersbach, H. Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast. 15, 559\u2013570 (2000).","journal-title":"Weather Forecast."},{"key":"980_CR29","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-021-27111-z","volume":"12","author":"D Traxl","year":"2021","unstructured":"Traxl, D., Boers, N., Rheinwalt, A. & Bookhagen, B. The role of cyclonic activity in tropical temperature-rainfall scaling. Nat. Commun. 12, 6732 (2021).","journal-title":"Nat. Commun."},{"key":"980_CR30","doi-asserted-by":"crossref","first-page":"98302","DOI":"10.1103\/PhysRevLett.126.098302","volume":"126","author":"T Beucler","year":"2021","unstructured":"Beucler, T. et al. Enforcing analytic constraints in neural networks emulating physical systems. Phys. Rev. Lett. 126, 98302 (2021).","journal-title":"Phys. Rev. Lett."},{"key":"980_CR31","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1145\/3381831","volume":"63","author":"R Schwartz","year":"2020","unstructured":"Schwartz, R., Dodge, J., Smith, N. A. & Etzioni, O. Green AI. Commun. ACM 63, 54\u201363 (2020).","journal-title":"Commun. ACM"},{"key":"980_CR32","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1038\/s41586-024-08252-9","volume":"637","author":"I Price","year":"2025","unstructured":"Price, I. et al. Probabilistic weather forecasting with machine learning. Nature 637, 84\u201390 (2025).","journal-title":"Nature"},{"key":"980_CR33","unstructured":"Huang, X. et al. Blue noise for diffusion models. In ACM SIGGRAPH (eds Burbano, A. et al.) 1\u201311 (Association for Computing Machinery, 2024)."},{"key":"980_CR34","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","volume":"146","author":"H Hersbach","year":"2020","unstructured":"Hersbach, H. et al. The ERA5 global reanalysis. Q. J. R. Meteorol. Soc. 146, 1999\u20132049 (2020).","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"980_CR35","doi-asserted-by":"crossref","first-page":"4117","DOI":"10.5194\/gmd-14-4117-2021","volume":"14","author":"M Dr\u00fcke","year":"2021","unstructured":"Dr\u00fcke, M. et al. CM2Mc-LPJmL v1.0: biophysical coupling of a process-based dynamic vegetation model with managed land to a general circulation model. Geosci. Model Dev. 14, 4117\u20134141 (2021).","journal-title":"Geosci. Model Dev."},{"key":"980_CR36","doi-asserted-by":"crossref","first-page":"e2019MS002015","DOI":"10.1029\/2019MS002015","volume":"12","author":"JP Dunne","year":"2020","unstructured":"Dunne, J. P. et al. The GFDL Earth System Model Version 4.1 (GFDL-ESM 4.1): overall coupled model description and simulation characteristics. J. Adv. Model. Earth Syst. 12, e2019MS002015 (2020).","journal-title":"J. Adv. Model. Earth Syst."},{"key":"980_CR37","doi-asserted-by":"crossref","first-page":"6323","DOI":"10.21105\/joss.06323","volume":"9","author":"M Kl\u00f6wer","year":"2024","unstructured":"Kl\u00f6wer, M. et al. SpeedyWeather.jl: reinventing atmospheric generalcirculation models towards interactivity and extensibility. J. Open Source Softw. 9, 6323 (2024).","journal-title":"J. Open Source Softw."},{"key":"980_CR38","unstructured":"Song, Y. & Ermon, S. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems (eds Wallach, H. M. et al) 11918\u201311930 (Curran Associates, 2019)."},{"key":"980_CR39","unstructured":"Song, J., Meng, C. & Ermon, S. Denoising Diffusion Implicit Models. In International Conference on Learning Representations 6323 (The Open Journal, 2021)."},{"key":"980_CR40","unstructured":"Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems (eds Larochelle, H. et al.) 6840\u20136851 (NeurIPS, 2020)."},{"key":"980_CR41","first-page":"2617\u20132680","volume":"22","author":"G Papamakarios","year":"2021","unstructured":"Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S. & Lakshminarayanan, B. Normalizing flows for probabilistic modeling and inference. J. Mach. Learn. Res. 22, 2617\u20132680 (2021).","journal-title":"J. Mach. Learn. Res."},{"key":"980_CR42","doi-asserted-by":"crossref","unstructured":"Zhang, R., Isola, P., Efros, A. A., Shechtman, E. & Wang, O. The unreasonable effectiveness of deep features as a perceptual metric. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 586\u2013595 (IEEE, 2018).","DOI":"10.1109\/CVPR.2018.00068"},{"key":"980_CR43","unstructured":"Lessig, C. et al. AtmoRep: a stochastic model of atmosphere dynamics using large scale representation learning. Preprint at http:\/\/arxiv.org\/abs\/2308.13280 (2023)."},{"key":"980_CR44","unstructured":"Grill, J. B. et al. Bootstrap your own latent\u2014a new approach to self-supervised learning. In Advances in Neural Information Processing Systems (eds Larochelle, M. e al.) 21271\u201321284 (Curran Associates, 2020)."},{"key":"980_CR45","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P. & Brox, T. U-Net: convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention\u2014MICCAI 2015. Lecture Notes in Computer Science (eds Navab, N. et al.) 234\u2013241 (Springer, 2015).","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"980_CR46","unstructured":"Kingma, D. P. & Ba, J. L. Adam: a method for stochastic optimization. In 3rd International Conference on Learning Representations ICLR 2015\u2014Conference Track Proc. 1\u201315 (ICLR, 2015)."},{"key":"980_CR47","unstructured":"Liu, L. et al. On the variance of the adaptive learning rate and beyond. In 8th International Conference on Learning Representations (OpenReview.net, 2020)."},{"key":"980_CR48","unstructured":"Rissanen, S., Heinonen, M. & Solin, A. Generative modelling with inverse heat dissipation. In 11th International Conference on Learning Representations (OpenReview.net, 2023)."},{"key":"980_CR49","doi-asserted-by":"publisher","unstructured":"Dr\u00fcke, M. Output data for the GMD publication gmd-2020-436. Zenodo https:\/\/doi.org\/10.5281\/zenodo.4683086 (2021).","DOI":"10.5281\/zenodo.4683086"},{"key":"980_CR50","unstructured":"Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32, 1\u201312 (2019)."},{"key":"980_CR51","doi-asserted-by":"publisher","unstructured":"Hess, P. p-hss\/consistency-climate-downscaling: pre-publication release. Zenodo https:\/\/doi.org\/10.5281\/zenodo.14203092 (2024).","DOI":"10.5281\/zenodo.14203092"},{"key":"980_CR52","doi-asserted-by":"publisher","unstructured":"Hess, P. Fast, scale-adaptive, and uncertainty-aware downscaling of earth system model fields with generative machine learning. Code Ocean https:\/\/doi.org\/10.24433\/CO.2150269.v1 (2024).","DOI":"10.24433\/CO.2150269.v1"}],"container-title":["Nature Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s42256-025-00980-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-025-00980-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s42256-025-00980-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T23:19:17Z","timestamp":1742858357000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s42256-025-00980-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,13]]},"references-count":52,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["980"],"URL":"https:\/\/doi.org\/10.1038\/s42256-025-00980-5","relation":{},"ISSN":["2522-5839"],"issn-type":[{"value":"2522-5839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,13]]},"assertion":[{"value":"1 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}