{"id":"https://openalex.org/W2995926841","doi":"https://doi.org/10.3390/e25101367","title":"Learning Energy-Based Models in High-Dimensional Spaces with Multiscale Denoising-Score Matching","display_name":"Learning Energy-Based Models in High-Dimensional Spaces with Multiscale Denoising-Score Matching","publication_year":2023,"publication_date":"2023-09-22","ids":{"openalex":"https://openalex.org/W2995926841","doi":"https://doi.org/10.3390/e25101367","mag":"2995926841","pmid":"https://pubmed.ncbi.nlm.nih.gov/37895489"},"language":"en","primary_location":{"id":"doi:10.3390/e25101367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101367","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1367/pdf?version=1695373810","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/10/1367/pdf?version=1695373810","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012657557","display_name":"Zengyi Li","orcid":"https://orcid.org/0000-0002-3720-0108"},"institutions":[{"id":"https://openalex.org/I4210145836","display_name":"Center for Theoretical Biological Physics","ror":"https://ror.org/04hfg7v94","country_code":"US","type":"facility","lineage":["https://openalex.org/I12912129","https://openalex.org/I181547552","https://openalex.org/I2801539370","https://openalex.org/I4210145836","https://openalex.org/I44461941","https://openalex.org/I74775410"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zengyi Li","raw_affiliation_strings":["Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA","Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA"],"raw_orcid":"https://orcid.org/0000-0002-3720-0108","affiliations":[{"raw_affiliation_string":"Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I4210145836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013970773","display_name":"Yubei Chen","orcid":"https://orcid.org/0000-0002-8930-3512"},"institutions":[{"id":"https://openalex.org/I4210145836","display_name":"Center for Theoretical Biological Physics","ror":"https://ror.org/04hfg7v94","country_code":"US","type":"facility","lineage":["https://openalex.org/I12912129","https://openalex.org/I181547552","https://openalex.org/I2801539370","https://openalex.org/I4210145836","https://openalex.org/I44461941","https://openalex.org/I74775410"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yubei Chen","raw_affiliation_strings":["Berkeley AI Research, University of California Berkeley, Berkeley, CA 94720, USA","Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA"],"raw_orcid":"https://orcid.org/0000-0002-8930-3512","affiliations":[{"raw_affiliation_string":"Berkeley AI Research, University of California Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I4210145836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085896415","display_name":"Friedrich T. Sommer","orcid":"https://orcid.org/0000-0002-6738-9263"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]},{"id":"https://openalex.org/I4210145836","display_name":"Center for Theoretical Biological Physics","ror":"https://ror.org/04hfg7v94","country_code":"US","type":"facility","lineage":["https://openalex.org/I12912129","https://openalex.org/I181547552","https://openalex.org/I2801539370","https://openalex.org/I4210145836","https://openalex.org/I44461941","https://openalex.org/I74775410"]},{"id":"https://openalex.org/I881441977","display_name":"Los Angeles Mission College","ror":"https://ror.org/01stcbz02","country_code":"US","type":"education","lineage":["https://openalex.org/I2802998804","https://openalex.org/I881441977"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Friedrich T. Sommer","raw_affiliation_strings":["Helen Wills Neuroscience Institute, University of California Berkeley, Berkeley, CA 94720, USA","Neuromorphic Computing Group, Intel Labs, 2200 Mission College Blvd., Santa Clara, CA 95054, USA","Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Helen Wills Neuroscience Institute, University of California Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Neuromorphic Computing Group, Intel Labs, 2200 Mission College Blvd., Santa Clara, CA 95054, USA","institution_ids":["https://openalex.org/I881441977","https://openalex.org/I1343180700"]},{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I4210145836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012657557"],"corresponding_institution_ids":["https://openalex.org/I4210145836","https://openalex.org/I95457486"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4254,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.59678049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"10","first_page":"1367","last_page":"1367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.7191663980484009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6537810564041138},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6494748592376709},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6090303659439087},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5845435261726379},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5652279853820801},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5452563762664795},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3677555322647095},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3675633370876312},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.23516413569450378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23253697156906128},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19830453395843506}],"concepts":[{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.7191663980484009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6537810564041138},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6494748592376709},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6090303659439087},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5845435261726379},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5652279853820801},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5452563762664795},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3677555322647095},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3675633370876312},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.23516413569450378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23253697156906128},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19830453395843506}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e25101367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101367","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1367/pdf?version=1695373810","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:37895489","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37895489","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:1910.07762","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.07762","pdf_url":"https://arxiv.org/pdf/1910.07762","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:10606347","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10606347","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10606347/pdf/entropy-25-01367.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:aad14cc055214b8cb4facf10fef2acf3","is_oa":true,"landing_page_url":"https://doaj.org/article/aad14cc055214b8cb4facf10fef2acf3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 10, p 1367 (2023)","raw_type":"article"},{"id":"doi:10.48550/arxiv.1910.07762","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.07762","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3390/e25101367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25101367","pdf_url":"https://www.mdpi.com/1099-4300/25/10/1367/pdf?version=1695373810","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5}],"awards":[{"id":"https://openalex.org/G4230570162","display_name":null,"funder_award_id":"R01 EB026955","funder_id":"https://openalex.org/F4320337363","funder_display_name":"National Institute of Biomedical Imaging and Bioengineering"},{"id":"https://openalex.org/G6279555096","display_name":null,"funder_award_id":"R01-EB026955","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8850892312","display_name":"RI: Small: Extracting and Understanding Sparse Structure in Spatiotemporal Data in Neuroscience and Other Applications","funder_award_id":"1718991","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320307102","display_name":"Intel Corporation","ror":"https://ror.org/01ek73717"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337363","display_name":"National Institute of Biomedical Imaging and Bioengineering","ror":"https://ror.org/00372qc85"},{"id":"https://openalex.org/F4320338021","display_name":"Iowa Nutrient Research Center, College of Agriculture and Life Sciences, Iowa State University","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995926841.pdf"},"referenced_works_count":94,"referenced_works":["https://openalex.org/W237147528","https://openalex.org/W602904462","https://openalex.org/W1505878979","https://openalex.org/W1513873506","https://openalex.org/W1515020792","https://openalex.org/W1551558821","https://openalex.org/W1583912456","https://openalex.org/W1693289132","https://openalex.org/W1834627138","https://openalex.org/W1939739483","https://openalex.org/W2001141328","https://openalex.org/W2013035813","https://openalex.org/W2020999234","https://openalex.org/W2024060531","https://openalex.org/W2053186076","https://openalex.org/W2071048859","https://openalex.org/W2079182758","https://openalex.org/W2096192494","https://openalex.org/W2099471712","https://openalex.org/W2116064496","https://openalex.org/W2116825644","https://openalex.org/W2118020555","https://openalex.org/W2119938170","https://openalex.org/W2122410182","https://openalex.org/W2136111243","https://openalex.org/W2144732271","https://openalex.org/W2145094598","https://openalex.org/W2156047073","https://openalex.org/W2157404321","https://openalex.org/W2161914416","https://openalex.org/W2167433878","https://openalex.org/W2185528074","https://openalex.org/W2194775991","https://openalex.org/W2267126114","https://openalex.org/W2294861638","https://openalex.org/W2302255633","https://openalex.org/W2398119937","https://openalex.org/W2594103415","https://openalex.org/W2623293810","https://openalex.org/W2768501777","https://openalex.org/W2782980316","https://openalex.org/W2785678896","https://openalex.org/W2787248994","https://openalex.org/W2789367656","https://openalex.org/W2804123849","https://openalex.org/W2804821933","https://openalex.org/W2895363208","https://openalex.org/W2896687685","https://openalex.org/W2898631838","https://openalex.org/W2914221386","https://openalex.org/W2922772346","https://openalex.org/W2938608316","https://openalex.org/W2946117724","https://openalex.org/W2948700496","https://openalex.org/W2949561945","https://openalex.org/W2953318193","https://openalex.org/W2954040150","https://openalex.org/W2959300817","https://openalex.org/W2962676938","https://openalex.org/W2963139417","https://openalex.org/W2963344330","https://openalex.org/W2963373786","https://openalex.org/W2963527611","https://openalex.org/W2963540976","https://openalex.org/W2963546708","https://openalex.org/W2963836885","https://openalex.org/W2963848397","https://openalex.org/W2963981733","https://openalex.org/W2964020555","https://openalex.org/W2964148965","https://openalex.org/W2964378242","https://openalex.org/W2970641149","https://openalex.org/W2971034910","https://openalex.org/W2997570648","https://openalex.org/W2997574889","https://openalex.org/W2998462233","https://openalex.org/W3004970274","https://openalex.org/W3118608800","https://openalex.org/W4241385190","https://openalex.org/W4250954493","https://openalex.org/W4288412300","https://openalex.org/W4289761690","https://openalex.org/W4293775665","https://openalex.org/W4297712886","https://openalex.org/W4301206121","https://openalex.org/W4320013936","https://openalex.org/W4365817089","https://openalex.org/W6680375596","https://openalex.org/W6681096077","https://openalex.org/W6686557994","https://openalex.org/W6687483927","https://openalex.org/W6718379498","https://openalex.org/W6747733185","https://openalex.org/W6755609140"],"related_works":["https://openalex.org/W3006513224","https://openalex.org/W2046456988","https://openalex.org/W2357409937","https://openalex.org/W2510582230","https://openalex.org/W2978674666","https://openalex.org/W2074430941","https://openalex.org/W2113096305","https://openalex.org/W2772305933","https://openalex.org/W3034789145","https://openalex.org/W4367628250"],"abstract_inverted_index":{"Energy-based":[0],"models":[1,80,94],"(EBMs)":[2],"assign":[3],"an":[4,135,199],"unnormalized":[5],"log":[6],"probability":[7],"to":[8,67,175],"data":[9,22,72,88,102,124,151],"samples.":[10],"This":[11],"functionality":[12],"has":[13,63],"a":[14,106,110,160,171,183],"variety":[15],"of":[16,36,92,100,130],"applications,":[17],"such":[18,93,178],"as":[19,179],"sample":[20,24,98,119],"synthesis,":[21],"denoising,":[23],"restoration,":[25],"outlier":[26],"detection,":[27],"Bayesian":[28],"reasoning":[29],"and":[30,83,137,181,195],"many":[31],"more.":[32],"But,":[33],"the":[34,50,96,150],"training":[35,142],"EBMs":[37],"using":[38],"standard":[39],"maximum":[40],"likelihood":[41],"is":[42,147,153],"extremely":[43],"slow":[44],"because":[45],"it":[46],"requires":[47],"sampling":[48],"from":[49],"model":[51,112,169,190],"distribution.":[52],"Score":[53],"matching":[54,62,116],"potentially":[55],"alleviates":[56],"this":[57,156],"problem.":[58],"In":[59],"particular,":[60],"denoising-score":[61,115,166],"been":[64],"successfully":[65],"used":[66],"train":[68],"EBMs.":[69,187],"Using":[70],"noisy":[71],"samples":[73,125],"with":[74,123,127,143,164],"one":[75],"fixed":[76],"noise":[77,145],"level,":[78],"these":[79],"learn":[81],"fast":[82],"yield":[84],"good":[85],"results":[86],"in":[87,95],"denoising.":[89],"However,":[90],"demonstrations":[91],"high-quality":[97],"synthesis":[99,120],"high-dimensional":[101],"were":[103],"lacking.":[104],"Recently,":[105],"paper":[107],"showed":[108],"that":[109,141],"generative":[111],"trained":[113,122,163],"by":[114],"accomplishes":[117],"excellent":[118],"when":[121,149],"corrupted":[126],"multiple":[128,144],"levels":[129,146],"noise.":[131],"Here":[132],"we":[133,158],"provide":[134],"analysis":[136],"empirical":[138],"evidence":[139],"showing":[140],"necessary":[148],"dimension":[152],"high.":[154],"Leveraging":[155],"insight,":[157],"propose":[159],"novel":[161],"EBM":[162],"multiscale":[165],"matching.":[167],"Our":[168],"exhibits":[170],"data-generation":[172],"performance":[173],"comparable":[174],"state-of-the-art":[176],"techniques":[177],"GANs":[180],"sets":[182],"new":[184],"baseline":[185],"for":[186],"The":[188],"proposed":[189],"also":[191],"provides":[192],"density":[193],"information":[194],"performs":[196],"well":[197],"on":[198],"image-inpainting":[200],"task.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2019-12-26T00:00:00"}
