{"id":"https://openalex.org/W7214280689","doi":"https://doi.org/10.48550/arxiv.2609.29216","title":"FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference","display_name":"FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214280689","doi":"https://doi.org/10.48550/arxiv.2609.29216"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29216","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29216","pdf_url":"https://arxiv.org/pdf/2609.29216","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152846544","display_name":"Gatien S\u00e9guy","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210136613","display_name":"Laboratoire des syst\u00e8mes et applications des technologies de l'information et de l'\u00e9nergie","ror":"https://ror.org/03vam5b06","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I124158823","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I2800365227","https://openalex.org/I4210134562","https://openalex.org/I4210136613","https://openalex.org/I4210142324","https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S\u00e9guy, Gatien","raw_affiliation_strings":["SATIE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SATIE","institution_ids":["https://openalex.org/I4210136613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039649943","display_name":"Thomas Rodet","orcid":"https://orcid.org/0000-0003-0473-9390","observed_orcids":["https://orcid.org/0000-0003-0473-9390"]},"institutions":[{"id":"https://openalex.org/I4210136613","display_name":"Laboratoire des syst\u00e8mes et applications des technologies de l'information et de l'\u00e9nergie","ror":"https://ror.org/03vam5b06","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I124158823","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I2800365227","https://openalex.org/I4210134562","https://openalex.org/I4210136613","https://openalex.org/I4210142324","https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rodet, Thomas","raw_affiliation_strings":["SATIE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SATIE","institution_ids":["https://openalex.org/I4210136613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210136613"],"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.8335000276565552,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.8335000276565552,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.09809999912977219,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.029400000348687172,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-inverse-problems","display_name":"linear inverse problems","score":0.9169999957084656},{"id":"https://openalex.org/keywords/diffusion-posterior-sampling","display_name":"diffusion posterior sampling","score":0.6629999876022339},{"id":"https://openalex.org/keywords/high-dimensional-inverse-problems","display_name":"high-dimensional inverse problems","score":0.6439999938011169},{"id":"https://openalex.org/keywords/image-denoising","display_name":"image denoising","score":0.6740000247955322},{"id":"https://openalex.org/keywords/celeba-hq","display_name":"CelebA-HQ","score":0.8230000138282776}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6176000237464905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5453000068664551},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.5360000133514404},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5175999999046326},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.4975000023841858},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4973999857902527},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.47940000891685486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45660001039505005},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41769999265670776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4153999984264374},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3582000136375427},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33899998664855957},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.29216","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29216","pdf_url":"https://arxiv.org/pdf/2609.29216","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":"pmh:oai:HAL:hal-05758586v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05758586","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.29216","doi":"https://doi.org/10.48550/arxiv.2609.29216","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29216","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:2609.29216","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29216","pdf_url":"https://arxiv.org/pdf/2609.29216","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214280689.pdf","grobid_xml":"https://content.openalex.org/works/W7214280689.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4403087461"],"related_works":["https://openalex.org/W4407231311","https://openalex.org/W4415795379","https://openalex.org/W7134852357","https://openalex.org/W4412836821","https://openalex.org/W7161560004","https://openalex.org/W4406271031","https://openalex.org/W4404889644","https://openalex.org/W4392971877","https://openalex.org/W4318719024","https://openalex.org/W7203689795"],"abstract_inverted_index":{"Diffusion":[0,14,20],"models":[1],"are":[2,138],"powerful":[3],"priors":[4],"for":[5,255],"linear":[6],"inverse":[7,148],"problems,":[8],"but":[9],"the":[10,32,50,72,78,104,109,128,132,139,142,159,173,177,188,193,205,208,212,229,252,260],"reference":[11],"guidance":[12,283],"methods,":[13],"Posterior":[15],"Sampling":[16],"(DPS)":[17],"and":[18,75,81,141,190,225,242,274],"Pseudoinverse-Guided":[19],"Models":[21],"($\u03a0$GDM),":[22],"rely":[23],"on":[24,63,146,187],"scalar":[25],"hyperparameters":[26],"tuned":[27],"per":[28],"task,":[29],"usually":[30],"against":[31,251],"ground":[33,133,253],"truth.":[34],"We":[35],"introduce":[36],"FB-GDM,":[37],"a":[38,57,118,220,239,280],"fully-Bayesian":[39],"guided":[40],"diffusion":[41],"method":[42],"that":[43,61],"removes":[44],"this":[45,270],"calibration":[46],"step.":[47,94],"Starting":[48],"from":[49,158],"Gaussian":[51],"approximation":[52,74],"of":[53,106],"$\u03a0$GDM,":[54],"we":[55],"derive":[56],"closed-form":[58],"conditional":[59],"score":[60],"depends":[62],"two":[64,151],"precision":[65,155],"parameters":[66],"(inverse":[67],"variances),":[68],"one":[69,76,122],"associated":[70],"with":[71,77,103,232],"denoising":[73],"observation":[79,140,160],"likelihood,":[80],"treat":[82],"them":[83],"as":[84],"latent":[85],"variables":[86],"inferred":[87,157],"by":[88,181],"variational":[89],"inference":[90,110],"at":[91,113,117,167,238],"each":[92,99,256],"reverse":[93],"A":[95],"separable":[96],"factorization":[97],"makes":[98],"update":[100],"scale":[101,241],"linearly":[102],"number":[105],"pixels,":[107],"so":[108],"stays":[111,217,244],"tractable":[112],"full":[114],"image":[115,213],"resolution,":[116],"cost":[119],"comparable":[120],"to":[121,164,183,191,219,264],"$\u03a0$GDM":[123,166,195,222,243],"run.":[124],"FB-GDM":[125,163,201,277],"requires":[126],"neither":[127],"noise":[129,179,209],"level":[130],"nor":[131],"truth:":[134],"its":[135,168,267],"only":[136,246],"inputs":[137],"forward":[143,206],"operator.":[144],"Experiments":[145],"CelebA-HQ":[147],"problems":[149],"establish":[150],"results.":[152],"(i)":[153],"The":[154],"parameters,":[156],"alone,":[161],"allow":[162],"outperform":[165],"nominal":[169],"setting,":[170],"even":[171],"when":[172,204],"latter":[174],"is":[175,202,249,262],"given":[176],"true":[178],"level,":[180,210],"up":[182],"14":[184],"dB":[185],"depending":[186],"operator,":[189,207],"match":[192],"ground-truth-calibrated":[194],"oracle":[196,223],"within":[197],"0.1":[198],"dB.":[199],"(ii)":[200],"robust":[203],"or":[211],"distribution":[214],"changes:":[215],"it":[216,248],"close":[218],"per-problem":[221],"throughout":[224],"does":[226],"not":[227],"exhibit":[228],"hallucinations":[230],"observed":[231],"DPS,":[233],"whereas":[234],"DPS":[235],"substantially":[236],"degrades":[237],"fixed":[240,281],"competitive":[245],"if":[247],"re-tuned":[250],"truth":[254],"new":[257],"problem.":[258],"When":[259],"prior":[261,275],"applied":[263],"images":[265],"outside":[266],"training":[268],"set,":[269],"re-balancing":[271],"between":[272],"data":[273],"keeps":[276],"faithful":[278],"where":[279],"face-prior":[282],"can":[284],"otherwise":[285],"hallucinate.":[286]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}