{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T03:28:41Z","timestamp":1782790121306,"version":"3.54.5"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T00:00:00Z","timestamp":1772496000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003500","name":"Universit\u00e0 degli Studi di Padova","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003500","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021856","name":"Ministero dell'Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["18\/09\/2024) \\u2013 CUP B53C24006570006"],"award-info":[{"award-number":["18\/09\/2024) \\u2013 CUP B53C24006570006"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021856","name":"Ministero dell'Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["1401"],"award-info":[{"award-number":["1401"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neurocomputing"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.neucom.2026.133197","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:17:48Z","timestamp":1772583468000},"page":"133197","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["D4: Distance diffusion for a truly equivariant molecular design"],"prefix":"10.1016","volume":"679","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6253-8450","authenticated-orcid":false,"given":"Samuel","family":"Cognolato","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2092-3577","authenticated-orcid":false,"given":"Davide","family":"Rigoni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Ballarini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luciano","family":"Serafini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Moro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8686-850X","authenticated-orcid":false,"given":"Alessandro","family":"Sperduti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"11","key":"10.1016\/j.neucom.2026.133197_bib0005","doi-asserted-by":"crossref","first-page":"6186","DOI":"10.3390\/ijms25116186","article-title":"Tumflow: an AI model for predicting new anticancer molecules","volume":"25","author":"Rigoni","year":"2024","journal-title":"Int. J. Mol. Sci."},{"issue":"4","key":"10.1016\/j.neucom.2026.133197_bib0010","doi-asserted-by":"crossref","DOI":"10.1136\/svn-2017-000101","article-title":"Artificial intelligence in healthcare: past, present and future","volume":"2","author":"Jiang","year":"2017","journal-title":"Stroke Vasc. Neurol."},{"key":"10.1016\/j.neucom.2026.133197_bib0015","series-title":"The Eleventh International Conference on Learning Representations, ICLR 2023","article-title":"Digress: discrete denoising diffusion for graph generation","author":"Vignac","year":"2023"},{"key":"10.1016\/j.neucom.2026.133197_bib0020","series-title":"27th European Conference on Artificial Intelligence, ECAI 2024","first-page":"3039","article-title":"IFH: a diffusion framework for flexible design of graph generative models","author":"Cognolato","year":"2024"},{"key":"10.1016\/j.neucom.2026.133197_bib0025","series-title":"IEEE SSCI","first-page":"729","article-title":"Conditional constrained graph variational autoencoders for molecule design","author":"Rigoni","year":"2020"},{"issue":"2","key":"10.1016\/j.neucom.2026.133197_bib0030","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s10994-024-06638-4","article-title":"Rgcvae: relational graph conditioned variational autoencoder for molecule design","volume":"114","author":"Rigoni","year":"2025","journal-title":"Mach. Learn."},{"key":"10.1016\/j.neucom.2026.133197_bib0035","series-title":"Midi: Mixed Graph and 3d Denoising Diffusion for Molecule Generation, ECML PKDD","first-page":"560","author":"Vignac","year":"2023"},{"key":"10.1016\/j.neucom.2026.133197_bib0040","first-page":"8867","article-title":"Equivariant diffusion for molecule generation in 3d, ICML","author":"Hoogeboom","year":"2022","journal-title":"PMLR"},{"key":"10.1016\/j.neucom.2026.133197_bib0045","author":"Thomas"},{"key":"10.1016\/j.neucom.2026.133197_bib0050","series-title":"The Eleventh International Conference on Learning Representations, ICLR 2023","article-title":"Equiformer: equivariant graph attention transformer for 3d atomistic graphs","author":"Liao","year":"2023"},{"key":"10.1016\/j.neucom.2026.133197_bib0055","first-page":"9323","article-title":"E(n) equivariant graph neural networks, ICML","author":"Satorras","year":"2021","journal-title":"PMLR"},{"key":"10.1016\/j.neucom.2026.133197_bib0060","first-page":"13757","article-title":"Geomol: torsional geometric generation of molecular 3d conformer ensembles","volume":"34","author":"Ganea","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133197_bib0065","series-title":"The Tenth International Conference on Learning Representations, ICLR","article-title":"Geodiff: a geometric diffusion model for molecular conformation generation","author":"Xu","year":"2022"},{"key":"10.1016\/j.neucom.2026.133197_bib0070","series-title":"AAAI Workshop on Deep Learning on Graphs: Methods and Applications","article-title":"A generalization of transformer networks to graphs","author":"Dwivedi","year":"2021"},{"issue":"2","key":"10.1016\/j.neucom.2026.133197_bib0075","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1021\/acscentsci.7b00572","article-title":"Automatic chemical design using a data-driven continuous representation of molecules","volume":"4","author":"G\u00f3mez-Bombarelli","year":"2018","journal-title":"ACS Cent. Sci."},{"key":"10.1016\/j.neucom.2026.133197_bib0080","series-title":"The Second International Conference on Learning Representations, ICLR","article-title":"Auto-encoding variational Bayes","author":"Kingma","year":"2014"},{"issue":"1","key":"10.1016\/j.neucom.2026.133197_bib0085","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1021\/ci00057a005","article-title":"Smiles, a chemical language and information system. 1. Introduction to methodology and encoding rules","volume":"28","author":"Weininger","year":"1988","journal-title":"J. Chem. Inf. Comput. Sci."},{"issue":"2","key":"10.1016\/j.neucom.2026.133197_bib0090","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1021\/ci00062a008","article-title":"Smiles. 2. Algorithm for generation of unique smiles notation","volume":"29","author":"Weininger","year":"1989","journal-title":"J. Chem. Inf. Comput. Sci."},{"issue":"3","key":"10.1016\/j.neucom.2026.133197_bib0095","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1021\/ci00067a005","article-title":"Smiles. 3. Depict. Graphical depiction of chemical structures","volume":"30","author":"Weininger","year":"1990","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"10.1016\/j.neucom.2026.133197_bib0100","first-page":"2323","article-title":"Junction tree variational autoencoder for molecular graph generation, ICML","author":"Jin","year":"2018","journal-title":"PMLR"},{"key":"10.1016\/j.neucom.2026.133197_bib0105","series-title":"Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","first-page":"617","article-title":"Moflow: an invertible flow model for generating molecular graphs","author":"Zang","year":"2020"},{"key":"10.1016\/j.neucom.2026.133197_bib0110","series-title":"International Conference on Learning Representations, ICLR","article-title":"Graphaf: a flow-based autoregressive model for molecular graph generation","author":"Shi","year":"2020"},{"key":"10.1016\/j.neucom.2026.133197_bib0115","series-title":"Molgan: an Implicit Generative Model for Small Molecular Graphs, ICML 2018 Workshop on Theoretical Foundations and Applications of Deep Generative Models","author":"De Cao","year":"2018"},{"key":"10.1016\/j.neucom.2026.133197_bib0120","first-page":"12454","article-title":"Argmax flows and multinomial diffusion: learning categorical distributions","volume":"34","author":"Hoogeboom","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133197_bib0125","series-title":"Proceedings of the AAAI Conference on Artificial Intelligence","first-page":"4302","article-title":"Conditional diffusion based on discrete graph structures for molecular graph generation","volume":"vol. 37","author":"Huang","year":"2023"},{"key":"10.1016\/j.neucom.2026.133197_bib0130","doi-asserted-by":"crossref","DOI":"10.1109\/TNNLS.2024.3416328","article-title":"Learning joint 2-d and 3-d graph diffusion models for complete molecule generation","author":"Huang","year":"2024","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.neucom.2026.133197_bib0135","series-title":"ICML","first-page":"1945","article-title":"Grammar variational autoencoder","author":"Kusner","year":"2017"},{"key":"10.1016\/j.neucom.2026.133197_bib0140","first-page":"6840","article-title":"Denoising diffusion probabilistic models","volume":"33","author":"Ho","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133197_bib0145","first-page":"8162","article-title":"Improved denoising diffusion probabilistic models, ICML","author":"Nichol","year":"2021","journal-title":"PMLR"},{"issue":"4","key":"10.1016\/j.neucom.2026.133197_bib0150","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF02288916","article-title":"Multidimensional scaling: i. Theory and method","volume":"17","author":"Torgerson","year":"1952","journal-title":"Psychometrika"},{"key":"10.1016\/j.neucom.2026.133197_bib0155","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0024-3795(88)90223-6","article-title":"Computing a nearest symmetric positive semidefinite matrix","volume":"103","author":"Higham","year":"1988","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"10.1016\/j.neucom.2026.133197_bib0160","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF02287916","article-title":"Discussion of a set of points in terms of their mutual distances","volume":"3","author":"Young","year":"1938","journal-title":"Psychometrika"},{"issue":"1","key":"10.1016\/j.neucom.2026.133197_bib0165","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/sdata.2014.22","article-title":"Quantum Chemistry structures and properties of 134 kilo molecules","volume":"1","author":"Ramakrishnan","year":"2014","journal-title":"Sci. Data"},{"issue":"25","key":"10.1016\/j.neucom.2026.133197_bib0170","doi-asserted-by":"crossref","first-page":"8732","DOI":"10.1021\/ja902302h","article-title":"970 million druglike small molecules for virtual screening in the chemical universe database gdb-13","volume":"131","author":"Blum","year":"2009","journal-title":"J. Am. Chem. Soc."},{"issue":"1","key":"10.1016\/j.neucom.2026.133197_bib0175","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1021\/ci049714+","article-title":"Zinc- a free database of commercially available compounds for virtual screening","volume":"45","author":"Irwin","year":"2005","journal-title":"J. Chem. Inf. Model."},{"issue":"11","key":"10.1016\/j.neucom.2026.133197_bib0180","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1021\/ci300415d","article-title":"Enumeration of 166 billion organic small molecules in the chemical universe database gdb-17","volume":"52","author":"Ruddigkeit","year":"2012","journal-title":"J. Chem. Inf. Model."},{"issue":"25","key":"10.1016\/j.neucom.2026.133197_bib0185","doi-asserted-by":"crossref","first-page":"10024","DOI":"10.1021\/ja00051a040","article-title":"Uff, a full periodic table force field for molecular mechanics and molecular dynamics simulations","volume":"114","author":"Rapp\u00e9","year":"1992","journal-title":"J. Am. Chem. Soc."},{"issue":"1\u201379","key":"10.1016\/j.neucom.2026.133197_bib0190","first-page":"4","article-title":"Rdkit documentation","volume":"1","author":"Landrum","year":"2013","journal-title":"Release"},{"key":"10.1016\/j.neucom.2026.133197_bib0195","series-title":"A Systematic Assessment of Deep Learning Models for Molecule Generation","first-page":"547","author":"Rigoni","year":"2020"},{"key":"10.1016\/j.neucom.2026.133197_bib0200","article-title":"Are gans created equal? A large-scale study","volume":"31","author":"Lucic","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"3","key":"10.1016\/j.neucom.2026.133197_bib0205","first-page":"64","article-title":"Markov processes over denumerable products of spaces, describing large systems of automata","volume":"5","author":"Vaserstein","year":"1969","journal-title":"Probl. Peredachi Inf."},{"key":"10.1016\/j.neucom.2026.133197_bib0210","article-title":"Principal neighbourhood aggregation for graph nets","volume":"33","author":"Corso","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"10.1016\/j.neucom.2026.133197_bib0215","series-title":"Proceedings of the AAAI Conference on Artificial Intelligence","article-title":"Film: visual reasoning with a general conditioning layer","volume":"vol. 32","author":"Perez","year":"2018"},{"key":"10.1016\/j.neucom.2026.133197_bib0220","series-title":"Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems","first-page":"929","article-title":"Pytorch 2: faster machine learning through dynamic Python bytecode transformation and graph compilation","volume":"vol. 2","author":"Ansel","year":"2024"},{"key":"10.1016\/j.neucom.2026.133197_bib0225","series-title":"Pytorch Lightning, GitHub 3","author":"Falcon","year":"2019"}],"container-title":["Neurocomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226005941?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0925231226005941?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T16:12:00Z","timestamp":1776096720000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0925231226005941"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":45,"alternative-id":["S0925231226005941"],"URL":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133197","relation":{},"ISSN":["0925-2312"],"issn-type":[{"value":"0925-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"D4: Distance diffusion for a truly equivariant molecular design","name":"articletitle","label":"Article Title"},{"value":"Neurocomputing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neucom.2026.133197","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"133197"}}