{"id":"https://openalex.org/W7139919788","doi":"https://doi.org/10.48550/arxiv.2603.18992","title":"Foundations of Schr\u00f6dinger Bridges for Generative Modeling","display_name":"Foundations of Schr\u00f6dinger Bridges for Generative Modeling","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7139919788","doi":"https://doi.org/10.48550/arxiv.2603.18992"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.18992","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18992","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.18992","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130245083","display_name":"Sophia Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tang, Sophia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5130245083"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.1500999927520752,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.1500999927520752,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.12470000237226486,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.09200000017881393,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.6938999891281128},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.47290000319480896},{"id":"https://openalex.org/keywords/bridge","display_name":"Bridge (graph theory)","score":0.37560001015663147},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3736000061035156},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.35690000653266907},{"id":"https://openalex.org/keywords/framing","display_name":"Framing (construction)","score":0.34459999203681946},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.33889999985694885},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.32499998807907104}],"concepts":[{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.6938999891281128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5720999836921692},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.47290000319480896},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C169087156","wikidata":"https://www.wikidata.org/wiki/Q2131593","display_name":"Framing (construction)","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33550000190734863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.334199994802475},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.32499998807907104},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.323199987411499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C184408114","wikidata":"https://www.wikidata.org/wiki/Q1502022","display_name":"Generative Design","level":3,"score":0.31279999017715454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30790001153945923},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C5065155","wikidata":"https://www.wikidata.org/wiki/Q1185775","display_name":"Frame problem","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.257999986410141},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.18992","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18992","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.18992","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18992","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"At":[0],"the":[1,17,46,69,73],"core":[2],"of":[3,19,72],"modern":[4,96],"generative":[5,97],"modeling":[6],"frameworks,":[7],"including":[8],"diffusion":[9],"models,":[10,12],"score-based":[11],"and":[13,83,86,111,120],"flow":[14],"matching,":[15],"is":[16],"task":[18],"transforming":[20],"a":[21,26,39,62,101],"simple":[22],"prior":[23],"distribution":[24,29,56],"into":[25],"complex":[27],"target":[28],"through":[30],"stochastic":[31,52,81],"paths":[32],"in":[33],"probability":[34],"space.":[35],"Schr\u00f6dinger":[36,74,106],"bridges":[37,107],"provide":[38],"unifying":[40],"principle":[41],"underlying":[42],"these":[43,114],"approaches,":[44],"framing":[45],"problem":[47],"as":[48],"determining":[49],"an":[50],"optimal":[51,79],"bridge":[53,75],"between":[54],"marginal":[55],"constraints":[57],"with":[58,92],"minimal-entropy":[59],"deviations":[60],"from":[61,108],"pre-defined":[63],"reference":[64],"process.":[65],"This":[66],"guide":[67],"develops":[68],"mathematical":[70],"foundations":[71],"problem,":[76],"drawing":[77],"on":[78,88],"transport,":[80],"control,":[82],"path-space":[84],"optimization,":[85],"focuses":[87],"its":[89],"dynamic":[90],"formulation":[91],"direct":[93],"connections":[94],"to":[95,118],"modeling.":[98],"We":[99],"build":[100],"comprehensive":[102],"toolkit":[103],"for":[104],"constructing":[105],"first":[109],"principles,":[110],"show":[112],"how":[113],"constructions":[115],"give":[116],"rise":[117],"generalized":[119],"task-specific":[121],"computational":[122],"methods.":[123]},"counts_by_year":[],"updated_date":"2026-03-21T06:36:02.116451","created_date":"2026-03-21T00:00:00"}