{"id":"https://openalex.org/W7160401210","doi":"https://doi.org/10.48550/arxiv.2605.02961","title":"Analytic Bridge Diffusions for Controlled Path Generation","display_name":"Analytic Bridge Diffusions for Controlled Path Generation","publication_year":2026,"publication_date":"2026-05-03","ids":{"openalex":"https://openalex.org/W7160401210","doi":"https://doi.org/10.48550/arxiv.2605.02961"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02961","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02961","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02961","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068974029","display_name":"Michael Chertkov","orcid":"https://orcid.org/0000-0002-6758-515X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chertkov, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068974029"],"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/T10581","display_name":"Neural dynamics and brain function","score":0.20350000262260437,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.20350000262260437,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.16750000417232513,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10982","display_name":"Motor Control and Adaptation","score":0.09000000357627869,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/terminal","display_name":"Terminal (telecommunication)","score":0.6953999996185303},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.6514999866485596},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.5277000069618225},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5267999768257141},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5109000205993652},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4661000072956085},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.46380001306533813},{"id":"https://openalex.org/keywords/brownian-bridge","display_name":"Brownian bridge","score":0.4634000062942505},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4350999891757965}],"concepts":[{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.6953999996185303},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.6514999866485596},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5277000069618225},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5267999768257141},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5109000205993652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47290000319480896},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.46380001306533813},{"id":"https://openalex.org/C78651780","wikidata":"https://www.wikidata.org/wiki/Q628309","display_name":"Brownian bridge","level":3,"score":0.4634000062942505},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4350999891757965},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.37869998812675476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37310001254081726},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35350000858306885},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3398999869823456},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.329800009727478},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3294000029563904},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.30140000581741333},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2540999948978424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02961","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02961","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:10.48550/arxiv.2605.02961","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02961","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Most":[0],"modern":[1],"bridge-diffusion":[2,203],"methods":[3],"achieve":[4],"finite-time":[5],"transport":[6,78,168],"by":[7,119],"specifying":[8],"an":[9,194],"interpolation,":[10],"Schr\u00f6dinger-bridge,":[11],"or":[12,21],"stochastic-control":[13,74,112],"objective":[14],"and":[15,37,47,60,95,102,125,130,170,177,204,218],"then":[16],"learning":[17],"the":[18,43,65,70,81,110,128,200],"associated":[19],"score":[20,214],"drift":[22],"field":[23],"with":[24,175,183],"a":[25,32,77,120,144,152,161,165,171,188,207],"neural":[26,62,202,212],"network.":[27],"In":[28,87,106],"contrast,":[29],"we":[30,108],"identify":[31],"restricted":[33],"but":[34,114],"sufficiently":[35],"broad":[36],"analytically":[38,195],"solvable":[39,196],"class":[40],"in":[41,52,64,210],"which":[42,211],"score,":[44],"intermediate":[45],"marginals,":[46],"protocol":[48],"gradients":[49],"are":[50],"available":[51],"closed":[53],"form":[54],"without":[55,61],"inner":[56],"stochastic":[57],"simulation":[58],"loops":[59],"networks":[63],"optimization":[66],"loop.":[67],"We":[68,157,190],"recast":[69],"classical":[71,88],"linear--quadratic--Gaussian":[72],"(LQG)":[73],"structure":[75],"as":[76,193],"problem":[79],"of":[80],"Path":[82],"Integral":[83],"Diffusion":[84],"(PID)":[85],"type.":[86],"LQG":[89],"control,":[90],"linear":[91],"dynamics,":[92],"Gaussian":[93,135],"noise,":[94],"quadratic":[96],"costs":[97],"lead":[98],"to":[99,133],"Riccati":[100],"equations":[101],"closed-form":[103],"optimal":[104],"feedback.":[105],"LQ-GM-PID,":[107],"retain":[109],"linear--quadratic":[111],"backbone,":[113],"replace":[115],"terminal":[116,122,131,147,180],"state":[117],"regulation":[118],"prescribed":[121],"probability":[123],"density":[124],"allow":[126],"both":[127],"initial":[129],"laws":[132],"be":[134,222],"Mixtures":[136],"(GM).":[137],"Moreover,":[138],"LQ-GM-PID":[139,192],"turns":[140],"bridge":[141],"diffusion":[142],"from":[143],"tool":[145,153],"for":[146,154,199],"target":[148],"matching":[149],"alone":[150],"into":[151],"path":[155],"shaping.":[156],"demonstrate":[158],"this":[159],"on":[160,187],"2D":[162,166],"corridor":[163],"task,":[164,169],"multi-entrance":[167],"high-dimensional":[172],"scaling":[173],"study":[174],"$d=32$":[176],"$M=16$":[178],"Gaussian-mixture":[179],"modes,":[181],"all":[182],"sub-50\\,ms":[184],"analytic":[185],"precompute":[186],"laptop.":[189],"position":[191],"reference":[197],"model":[198],"state-of-the-art":[201],"generative-transport":[205],"methods:":[206],"controlled":[208],"setting":[209],"approximations,":[213],"estimates,":[215],"path-shaping":[216],"objectives,":[217],"protocol-learning":[219],"procedures":[220],"can":[221],"tested":[223],"against":[224],"exact":[225],"quantities.":[226]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-07T00:00:00"}