{"id":"https://openalex.org/W7220892142","doi":"https://doi.org/10.48550/arxiv.2610.09281","title":"Twist Flow for Inverse Problems","display_name":"Twist Flow for Inverse Problems","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220892142","doi":"https://doi.org/10.48550/arxiv.2610.09281"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09281","pdf_url":"https://arxiv.org/pdf/2610.09281","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/2610.09281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017565703","display_name":"Shiqin Zeng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zeng, Shiqin","raw_affiliation_strings":["Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157904809","display_name":"Zijun Deng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deng, Zijun","raw_affiliation_strings":["Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010780250","display_name":"Felix J. Herrmann","orcid":"https://orcid.org/0000-0003-1180-2167","observed_orcids":["https://orcid.org/0000-0003-1180-2167"]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Herrmann, Felix J.","raw_affiliation_strings":["Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130701444"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.6128000020980835,"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":0.6128000020980835,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.17759999632835388,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.10540000349283218,"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/bayesian-inversion","display_name":"Bayesian inversion","score":0.8849999904632568},{"id":"https://openalex.org/keywords/posterior-sampling","display_name":"posterior sampling","score":0.8619999885559082},{"id":"https://openalex.org/keywords/flow-matching","display_name":"flow matching","score":0.878000020980835},{"id":"https://openalex.org/keywords/multimodal-posterior","display_name":"multimodal posterior","score":0.5870000123977661},{"id":"https://openalex.org/keywords/conditional-generative-models","display_name":"conditional generative models","score":0.6140000224113464},{"id":"https://openalex.org/keywords/image-restoration","display_name":"image restoration","score":0.5189999938011169}],"concepts":[{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.7728000283241272},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5672000050544739},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5001999735832214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4943000078201294},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4535999894142151},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3792000114917755},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3637999892234802},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3612000048160553},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3521000146865845},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3271999955177307},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.3174999952316284},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.31610000133514404},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C191413810","wikidata":"https://www.wikidata.org/wiki/Q17100952","display_name":"Bayesian hierarchical modeling","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.29109999537467957},{"id":"https://openalex.org/C172849965","wikidata":"https://www.wikidata.org/wiki/Q3148875","display_name":"Reference frame","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.263700008392334},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.257099986076355},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09281","pdf_url":"https://arxiv.org/pdf/2610.09281","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.2610.09281","doi":"https://doi.org/10.48550/arxiv.2610.09281","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09281","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09281","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09281","pdf_url":"https://arxiv.org/pdf/2610.09281","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/W7220892142.pdf","grobid_xml":"https://content.openalex.org/works/W7220892142.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7220462101","https://openalex.org/W7214715932","https://openalex.org/W7165812628","https://openalex.org/W7221567941","https://openalex.org/W4414577602","https://openalex.org/W6923368896","https://openalex.org/W4417299022","https://openalex.org/W4411317422","https://openalex.org/W4390021847","https://openalex.org/W3042619499"],"abstract_inverted_index":{"In":[0],"Bayesian":[1],"inverse":[2,191],"problems,":[3],"posterior":[4,60,65,124,195,203,225],"sampling":[5],"requires":[6],"generating":[7],"samples":[8,54,168],"that":[9,88],"are":[10],"consistent":[11],"with":[12,134,152,193],"given":[13],"observations":[14],"while":[15,58,178,227],"capturing":[16],"the":[17,45,48,64,94,101,110,115,119,135,147,187,213],"range":[18],"of":[19,169],"plausible":[20],"solutions.":[21,79],"Direct":[22],"conditional":[23],"generative":[24],"models":[25],"introduce":[26],"latent":[27],"noise":[28],"to":[29,47,69,100,159,165,171],"model":[30],"this":[31],"ambiguity,":[32],"but":[33,164],"paired":[34],"inverse-problem":[35],"training":[36],"can":[37],"still":[38],"encourage":[39],"an":[40,84],"almost":[41],"deterministic":[42],"map":[43],"from":[44,93],"observation":[46,136,141,149,153,172,229],"target.":[49],"As":[50],"a":[51,90,129,139,206],"result,":[52],"generated":[53,167],"may":[55],"be":[56],"observation-consistent":[57],"under-representing":[59],"variability,":[61],"especially":[62],"when":[63],"is":[66,109,114,118,128,144,157],"multimodal,":[67],"leading":[68],"undercoverage,":[70],"mode":[71],"distortion,":[72],"or":[73],"artificial":[74],"transitions":[75],"between":[76],"distinct":[77],"feasible":[78],"We":[80,185,210],"propose":[81],"joint":[82,198],"twist-flow,":[83],"augmented":[85,95,102],"flow-matching":[86],"formulation":[87],"learns":[89],"continuous":[91],"transport":[92],"source":[96],"state":[97,104],"$(z_x,":[98],"y)$":[99],"terminal":[103],"$(x,":[105],"z_y)$.":[106],"Here":[107],"x":[108,170],"target":[111],"variable,":[112],"$y$":[113],"observation,":[116],"$z_x$":[117],"Gaussian":[120,130,140],"reference":[121,194],"coordinate":[122,132],"for":[123],"sampling,":[125],"and":[126,218],"$z_y$":[127,143],"likelihood-side":[131],"associated":[133,151],"branch.":[137],"Under":[138],"model,":[142],"motivated":[145],"by":[146],"normalized":[148],"residual":[150],"compatibility.":[154],"Its":[155],"role":[156],"not":[158],"replace":[160],"uncertainty":[161],"in":[162,181],"$x$,":[163],"couple":[166],"consistency,":[173],"helping":[174],"reduce":[175],"likelihood-inconsistent":[176],"variation":[177],"preserving":[179],"variability":[180,226],"weakly":[182],"constrained":[183],"directions.":[184],"validate":[186],"method":[188,214],"on":[189,215],"low-dimensional":[190],"problems":[192],"samples,":[196],"where":[197],"twist-flow":[199],"better":[200],"preserves":[201],"multimodal":[202],"support":[204],"than":[205],"direct":[207],"conditional-flow":[208],"baseline.":[209],"further":[211],"evaluate":[212],"image":[216],"restoration":[217],"seismic":[219],"subsurface":[220],"velocity-model":[221],"inversion,":[222],"showing":[223],"increased":[224],"maintaining":[228],"consistency.":[230]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-09T00:00:00"}