{"id":"https://openalex.org/W7213411495","doi":"https://doi.org/10.48550/arxiv.2609.17287","title":"Same Flow, Different Paths: Variance Reduction in Flow Matching","display_name":"Same Flow, Different Paths: Variance Reduction in Flow Matching","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213411495","doi":"https://doi.org/10.48550/arxiv.2609.17287"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17287","pdf_url":"https://arxiv.org/pdf/2609.17287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135847823","display_name":"Alexander Tyurin","orcid":"https://orcid.org/0000-0003-4963-8227","observed_orcids":["https://orcid.org/0000-0003-4963-8227"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tyurin, Alexander","raw_affiliation_strings":["AXXX , Moscow , Russia Applied AI Institute , Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AXXX , Moscow , Russia Applied AI Institute , Moscow , Russia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135847823"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8500999808311462,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.8500999808311462,"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"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.02810000069439411,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.020600000396370888,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flow-matching","display_name":"flow matching","score":0.9990000128746033},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"variance reduction","score":0.6660000085830688},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"stochastic gradient descent","score":0.8560000061988831},{"id":"https://openalex.org/keywords/path-choice","display_name":"path selection","score":0.7009999752044678},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.7289999723434448},{"id":"https://openalex.org/keywords/iteration-complexity","display_name":"iteration complexity","score":0.7089999914169312},{"id":"https://openalex.org/keywords/marginal-distributions","display_name":"marginal distributions","score":0.4729999899864197},{"id":"https://openalex.org/keywords/velocity-model","display_name":"velocity model","score":0.5170000195503235},{"id":"https://openalex.org/keywords/optimal-paths","display_name":"optimal paths","score":0.3569999933242798},{"id":"https://openalex.org/keywords/gaussian-mixture-model","display_name":"Gaussian mixture model","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7457000017166138},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5630999803543091},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.527899980545044},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5234000086784363},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5180000066757202},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4634999930858612},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46230000257492065},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.42399999499320984},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.358599990606308},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3280999958515167},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.2897000014781952},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.26100000739097595}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17287","pdf_url":"https://arxiv.org/pdf/2609.17287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.17287","doi":"https://doi.org/10.48550/arxiv.2609.17287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17287","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17287","pdf_url":"https://arxiv.org/pdf/2609.17287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213411495.pdf","grobid_xml":"https://content.openalex.org/works/W7213411495.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133482994","https://openalex.org/W7214106835","https://openalex.org/W7168262058","https://openalex.org/W7127922793","https://openalex.org/W7160907041","https://openalex.org/W7084126769","https://openalex.org/W7215063353","https://openalex.org/W7216013420","https://openalex.org/W7163085662","https://openalex.org/W7220967289"],"abstract_inverted_index":{"In":[0,32],"flow":[1],"matching":[2],"(FM),":[3],"a":[4,11,107,117,163],"velocity":[5,69,109],"model":[6,110],"$v_\u03b8$":[7],"is":[8,81,180],"trained":[9],"using":[10],"predefined":[12],"path":[13,41,86,134,160],"$g_t$":[14,87],"that":[15,60,82,135,177,210],"connects":[16],"data":[17],"and":[18,67,72,111,129,158,235],"noise":[19],"samples":[20],"(e.g.,":[21],"$g_t(x_0,":[22],"x_1)":[23],"=":[24],"(1":[25],"-":[26],"t)":[27],"x_0":[28],"+":[29],"t":[30],"x_1$).":[31],"this":[33,40,137,178],"work,":[34],"we":[35,115,203],"study":[36],"the":[37,48,55,62,74,83,91,98,103,121,143,151,167,193],"choice":[38,84],"of":[39,50,58,85,94],"from":[42,214],"an":[43,131,205],"optimization":[44],"perspective":[45],"by":[46,227],"analyzing":[47],"variance":[49,152,183],"stochastic":[51],"gradients.":[52],"We":[53,148,175],"consider":[54],"class":[56],"$G(p_t,v^\\star_t)$":[57],"paths":[59,141,217],"induce":[61],"same":[63,75,144],"marginal":[64,68],"distributions":[65],"$p_t$":[66],"field":[70],"$v^\\star_t$,":[71],"therefore":[73],"FM":[76,99,145,156],"objective.":[77],"Our":[78,222],"main":[79],"finding":[80],"can":[88,186,211],"fundamentally":[89],"change":[90],"convergence":[92],"rate":[93],"SGD,":[95],"even":[96],"when":[97],"objective":[100],"remains":[101],"exactly":[102],"same.":[104],"(i)":[105],"For":[106],"linear":[108,140],"one-dimensional":[112],"Gaussian":[113,230,232],"data,":[114,231],"derive":[116,204],"tight":[118],"bound":[119,138],"on":[120],"SGD":[122],"iteration":[123],"complexity":[124],"up":[125],"to":[126,154,172,188,218],"logarithmic":[127],"factors":[128],"find":[130],"analytically":[132],"optimal":[133],"minimizes":[136],"among":[139],"inducing":[142],"problem.":[146],"(ii)":[147],"then":[149],"extend":[150],"analysis":[153],"general":[155],"problems":[157],"formulate":[159],"selection":[161],"at":[162],"fixed":[164],"$\u03b8$":[165],"as":[166],"variance-minimization":[168],"problem":[169],"PathOpt$_\u03b8$,":[170],"constrained":[171],"$g_t\\in":[173],"G(p_t,v^\\star_t)$.":[174],"show":[176],"constraint":[179,194],"essential:":[181],"reducing":[182],"without":[184],"it":[185],"lead":[187],"slower":[189],"convergence.":[190],"(iii)":[191],"Since":[192],"$g_t":[195],"\\in":[196],"G(p_t,v^\\star_t)$":[197],"cannot":[198],"generally":[199],"be":[200,212,219],"verified":[201],"directly,":[202],"equivalent":[206],"formulation":[207],"with":[208,229],"constraints":[209],"estimated":[213],"samples,":[215],"allowing":[216],"found":[220],"numerically.":[221],"theoretical":[223],"results":[224],"are":[225],"supported":[226],"experiments":[228],"mixture":[233],"models,":[234],"real":[236],"datasets.":[237]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-17T00:00:00"}
