{"id":"https://openalex.org/W7165812628","doi":"https://doi.org/10.48550/arxiv.2606.24516","title":"What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View","display_name":"What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165812628","doi":"https://doi.org/10.48550/arxiv.2606.24516"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.24516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24516","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.24516","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139237518","display_name":"Jian Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Jian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139294091","display_name":"Delu Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Delu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139228615","display_name":"John Paisley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paisley, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139243832","display_name":"Qibin Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Qibin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11205","display_name":"Numerical methods in inverse problems","score":0.27300000190734863,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.27300000190734863,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1185000017285347,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.10400000214576721,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.7009000182151794},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.680400013923645},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.6062999963760376},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5769000053405762},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5702000260353088},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5539000034332275},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.47920000553131104},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.45590001344680786}],"concepts":[{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.7009000182151794},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.680400013923645},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.6062999963760376},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5769000053405762},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5702000260353088},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5539000034332275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4925000071525574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48730000853538513},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4740999937057495},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3837999999523163},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2574000060558319},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.24516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24516","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.24516","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.24516","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":"Preprint"},"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":{"A":[0,173],"growing":[1],"family":[2],"of":[3,71,98,160,210],"training-free":[4],"solvers":[5,126],"--":[6,16,47,61],"FlowDPS,":[7],"FLOWER,":[8],"PnP-Flow":[9,150],"and":[10,48,144,205,233],"their":[11],"diffusion":[12],"ancestors":[13],"(DPS,":[14],"DAPS)":[15],"repurpose":[17],"a":[18,29,68,80,86,96,104,178,219],"pretrained":[19],"flow-matching":[20],"prior":[21],"to":[22,32,136,152,191],"solve":[23],"imaging":[24],"inverse":[25,73],"problems":[26],"by":[27,95,103,214],"adding":[28],"measurement-guidance":[30],"term":[31],"the":[33,51,56,99,108,112,131,138,142,166,182,188,192,215],"deterministic":[34],"probability-flow":[35],"ODE.":[36],"Despite":[37],"strong":[38],"empirical":[39],"results,":[40],"what":[41],"these":[42],"per-step":[43],"corrections":[44],"actually":[45],"approximate":[46],"how":[49],"far":[50],"resulting":[52,167],"samples":[53,245],"are":[54],"from":[55],"true":[57,189],"posterior":[58,118,168,180,190,207,244],"$p(x\\mid":[59],"y)$":[60],"has":[62],"not":[63,102],"been":[64],"characterized.":[65],"We":[66],"give":[67],"posterior-transport":[69],"account":[70],"flow-based":[72],"problem":[74],"solving.":[75],"Our":[76],"starting":[77],"point":[78],"is":[79,92,225],"simple":[81],"but":[82],"consequential":[83],"fact:":[84],"for":[85],"\\emph{deterministic}":[87],"flow":[88],"prior,":[89],"Bayesian":[90],"conditioning":[91],"realized":[93],"entirely":[94],"\\emph{reweighting":[97],"source":[100,110,140,185],"distribution},":[101],"drift":[105],"correction;":[106],"pushing":[107],"reweighted":[109],"through":[111],"\\emph{unmodified}":[113],"velocity":[114],"field":[115,134],"yields":[116],"exact":[117],"samples.":[119],"From":[120],"this":[121,161],"we":[122,164,217],"show":[123],"that":[124,145,224,248],"trajectory-guidance":[125],"can":[127],"be":[128],"read":[129],"as":[130],"minimum-kinetic-energy":[132],"\\emph{correction}":[133],"needed":[135],"morph":[137],"unconditional":[139],"into":[141],"posterior,":[143],"FlowDPS":[146],"/":[147,149,155,157],"FLOWER":[148],"correspond":[151],"distinct":[153],"zeroth-order":[154],"Gaussian":[156],"proximal":[158],"approximations":[159],"single":[162],"object;":[163],"bound":[165],"bias":[169],"in":[170],"Wasserstein":[171],"distance.":[172],"controlled":[174],"$2$D":[175],"study":[176],"with":[177,246,250],"closed-form":[179],"confirms":[181],"theory":[183],"decisively:":[184],"reweighting":[186],"matches":[187],"Monte-Carlo":[193],"floor":[194],"on":[195],"every":[196],"metric,":[197],"whereas":[198],"trajectory":[199],"guidance":[200,211],"incurs":[201],"$200$--$800\\times$":[202],"larger":[203],"error":[204],"collapses":[206],"modes,":[208],"\\emph{regardless":[209],"strength}.":[212],"Guided":[213],"analysis":[216],"propose":[218],"cheap,":[220],"principled":[221],"velocity-correction":[222],"solver":[223],"competitive":[226],"across":[227],"two":[228,234],"in-domain":[229],"priors":[230],"(AFHQ,":[231],"CelebA)":[232],"out-of-distribution":[235],"settings":[236],"while,":[237],"unlike":[238],"point-estimate":[239],"source-space":[240],"optimizers,":[241],"producing":[242],"diverse":[243],"uncertainty":[247],"correlates":[249],"reconstruction":[251],"error.":[252]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-25T00:00:00"}