{"id":"https://openalex.org/W7164036198","doi":"https://doi.org/10.48550/arxiv.2606.08672","title":"Learning to Solve Generative ODEs Beyond the Linear Span","display_name":"Learning to Solve Generative ODEs Beyond the Linear Span","publication_year":2026,"publication_date":"2026-06-07","ids":{"openalex":"https://openalex.org/W7164036198","doi":"https://doi.org/10.48550/arxiv.2606.08672"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.08672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08672","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":null,"license_id":null,"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.2606.08672","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038433902","display_name":"Sihyeon Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Sihyeon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138220844","display_name":"Seunghun Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Seunghun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100779003","display_name":"Vikas Singh","orcid":"https://orcid.org/0000-0002-8355-6519"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Singh, Vikas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138282607","display_name":"Hyunwoo J. Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Hyunwoo J.","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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.7892000079154968,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.7892000079154968,"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":0.11840000003576279,"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/T12303","display_name":"Tensor decomposition and applications","score":0.017100000753998756,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/solver","display_name":"Solver","score":0.7671999931335449},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.694100022315979},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5249999761581421},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5077999830245972},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4781000018119812},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.4498000144958496},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.40939998626708984},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.3488999903202057}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7671999931335449},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.694100022315979},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6313999891281128},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5249999761581421},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.515999972820282},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5077999830245972},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4781000018119812},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.475600004196167},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4498000144958496},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.3488999903202057},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3434999883174896},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30979999899864197},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29280000925064087},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C121448008","wikidata":"https://www.wikidata.org/wiki/Q1755722","display_name":"Large eddy simulation","level":3,"score":0.25119999051094055},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.08672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08672","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.08672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08672","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Diffusion":[0],"and":[1,109,118,133,146,156,176],"flow":[2,154],"generative":[3],"models":[4],"sample":[5],"by":[6,25,79,125],"integrating":[7],"a":[8,43,86,95,101,111],"learned":[9,140],"ODE,":[10],"but":[11],"high":[12],"quality":[13],"still":[14],"requires":[15],"many":[16],"sequential":[17],"model":[18,36,136],"evaluations.":[19],"Solver":[20],"learning":[21],"reduces":[22],"this":[23,39,47],"cost":[24],"adapting":[26],"scalar":[27,80],"coefficients,":[28],"timesteps,":[29],"or":[30],"both,":[31],"while":[32,73],"keeping":[33],"the":[34,55,60,70,116,130,139],"backbone":[35],"fixed.":[37],"In":[38],"work,":[40],"we":[41],"identify":[42],"structural":[44],"bottleneck":[45],"in":[46,59],"update":[48,57],"family:":[49],"each":[50],"step":[51],"remains":[52],"span-limited.":[53],"Since":[54],"scalar-coefficient":[56,92],"lies":[58],"span":[61],"of":[62],"buffered":[63],"velocity":[64,119],"evaluations,":[65],"it":[66,168],"can":[67],"fit":[68],"only":[69,165],"in-span":[71,107],"component":[72],"leaving":[74],"any":[75],"out-of-span":[76],"residual":[77,97,113],"unreachable":[78],"recombination":[81],"alone.":[82],"We":[83],"propose":[84],"SpanLift,":[85],"lightweight":[87],"neural":[88],"solver":[89,104],"that":[90],"augments":[91],"updates":[93],"with":[94],"spatial":[96,112],"operator.":[98],"SpanLift":[99,159],"keeps":[100],"fixed":[102],"base":[103,144],"as":[105],"an":[106],"prior":[108],"learns":[110],"operator":[114,122],"over":[115],"state":[117],"buffer.":[120],"The":[121],"is":[123,147],"trained":[124],"endpoint":[126],"teacher":[127],"matching,":[128,155],"preserves":[129],"pretrained":[131],"backbone,":[132],"adds":[134],"no":[135],"NFEs.":[137],"Empirically,":[138],"correction":[141],"transfers":[142],"across":[143],"solvers":[145],"predominantly":[148],"out-of-span.":[149],"Across":[150],"pixel-space":[151],"diffusion,":[152],"latent":[153],"precipitation":[157],"nowcasting,":[158],"achieves":[160],"state-of-the-art":[161],"few-step":[162],"sampling.":[163],"With":[164],"3":[166],"NFE,":[167],"improves":[169],"CIFAR-10":[170],"FID":[171,178],"from":[172,179],"8.16":[173],"to":[174,181],"5.69":[175],"ImageNet":[177],"17.37":[180],"11.83.":[182]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-10T00:00:00"}