{"id":"https://openalex.org/W4415367114","doi":"https://doi.org/10.1109/isit63088.2025.11195578","title":"Score-Based Manifold Projection for Diffusion-Based Inverse Problems","display_name":"Score-Based Manifold Projection for Diffusion-Based Inverse Problems","publication_year":2025,"publication_date":"2025-06-22","ids":{"openalex":"https://openalex.org/W4415367114","doi":"https://doi.org/10.1109/isit63088.2025.11195578"},"language":null,"primary_location":{"id":"doi:10.1109/isit63088.2025.11195578","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015275944","display_name":"S. Hamidi","orcid":"https://orcid.org/0000-0002-6024-5515"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Shayan Mohajer Hamidi","raw_affiliation_strings":["University of Waterloo,Waterloo,ON,Canada,N2L 3G1"],"affiliations":[{"raw_affiliation_string":"University of Waterloo,Waterloo,ON,Canada,N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080794633","display_name":"En\u2010hui Yang","orcid":"https://orcid.org/0000-0003-1504-7584"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"En-Hui Yang","raw_affiliation_strings":["University of Waterloo,Waterloo,ON,Canada,N2L 3G1"],"affiliations":[{"raw_affiliation_string":"University of Waterloo,Waterloo,ON,Canada,N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5015275944"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38069914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9936000108718872,"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":0.9936000108718872,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7283999919891357},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6003000140190125},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5026000142097473},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5022000074386597},{"id":"https://openalex.org/keywords/diffusion-map","display_name":"Diffusion map","score":0.4966999888420105},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4684000015258789},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.4607999920845032},{"id":"https://openalex.org/keywords/manifold-alignment","display_name":"Manifold alignment","score":0.4259999990463257},{"id":"https://openalex.org/keywords/oblique-projection","display_name":"Oblique projection","score":0.42559999227523804}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7283999919891357},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6003000140190125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5532000064849854},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5026000142097473},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5022000074386597},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.4966999888420105},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4684000015258789},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.4607999920845032},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.4259999990463257},{"id":"https://openalex.org/C161666082","wikidata":"https://www.wikidata.org/wiki/Q14551923","display_name":"Oblique projection","level":3,"score":0.42559999227523804},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3896999955177307},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3849000036716461},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3772999942302704},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3659999966621399},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.3391999900341034},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3352999985218048},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C113364801","wikidata":"https://www.wikidata.org/wiki/Q26674","display_name":"High fidelity","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2680000066757202},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit63088.2025.11195578","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit63088.2025.11195578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2013035813","https://openalex.org/W2108598243","https://openalex.org/W2133665775","https://openalex.org/W2962770929","https://openalex.org/W2962785568","https://openalex.org/W4293203252","https://openalex.org/W4385801729","https://openalex.org/W4390873784","https://openalex.org/W4415367385"],"related_works":[],"abstract_inverted_index":{"Inverse":[0],"problems":[1],"such":[2],"as":[3,16],"inpainting,":[4,160],"deblurring,":[5,159],"and":[6,146,152,161],"super-resolution":[7],"benefit":[8],"significantly":[9],"from":[10],"generative":[11],"diffusion":[12,37,63,77,190],"models,":[13],"which":[14],"serve":[15],"powerful":[17],"learned":[18,126],"priors.":[19],"However,":[20],"incorporating":[21],"measurement-consistency":[22],"gradients":[23],"naively":[24],"can":[25],"push":[26],"the":[27,31,36,57,62,73,76,102,105,125,138,177,180],"intermediate":[28],"solutions":[29],"off":[30],"high-likelihood":[32],"manifold":[33,52,68,139,168],"encoded":[34],"by":[35],"model,":[38],"leading":[39],"to":[40,66,90,109,118,124,137,188],"artifacts":[41,173],"or":[42],"suboptimal":[43],"reconstructions.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48,71,130,148],"propose":[49],"a":[50,183],"scorebased":[51,167],"projection":[53,169],"framework":[54],"that":[55,75,132,166],"leverages":[56],"internal":[58],"score":[59,78],"function":[60],"of":[61,92,104,179],"model":[64],"itself":[65],"preserve":[67],"fidelity.":[69],"Specifically,":[70],"exploit":[72],"fact":[74],"<tex":[79,97,110],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80,98,111],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\boldsymbol{s}_{\\theta}(\\boldsymbol{x},":[81],"t)":[82],"\\approx":[83],"\\nabla_{\\boldsymbol{x}}":[84],"\\log":[85],"p_{t}(\\boldsymbol{x})$</tex>":[86],"is":[87],"ideally":[88],"orthogonal":[89],"manifolds":[91],"constant":[93],"log-likelihood":[94],"at":[95],"time":[96],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$t$</tex>.":[99],"By":[100],"removing":[101],"component":[103],"measurement":[106],"gradient":[107],"parallel":[108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\boldsymbol{s}_{\\theta}$</tex>,":[112],"our":[113,133],"method":[114],"constrains":[115],"each":[116],"update":[117],"remain":[119],"(to":[120],"first":[121],"order)":[122],"tangent":[123],"data":[127],"manifold.":[128],"Theoretically,":[129],"prove":[131],"approach":[134],"preserves":[135],"proximity":[136],"more":[140],"effectively":[141],"than":[142],"an":[143],"un-projected":[144],"update,":[145],"empirically,":[147],"demonstrate":[149],"improved":[150],"robustness":[151],"quality":[153],"on":[154],"various":[155],"inverse":[156],"problems,":[157],"including":[158],"super-resolution.":[162],"Our":[163],"results":[164],"show":[165],"not":[170],"only":[171],"reduces":[172],"but":[174],"also":[175],"maintains":[176],"fidelity":[178],"reconstructions,":[181],"offering":[182],"simple":[184],"yet":[185],"effective":[186],"enhancement":[187],"measurement-guided":[189],"solvers.":[191]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-21T00:00:00"}