{"id":"https://openalex.org/W7163002600","doi":"https://doi.org/10.48550/arxiv.2605.31106","title":"Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks","display_name":"Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks","publication_year":2026,"publication_date":"2026-05-29","ids":{"openalex":"https://openalex.org/W7163002600","doi":"https://doi.org/10.48550/arxiv.2605.31106"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.31106","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31106","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,"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.2605.31106","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114633536","display_name":"Gyeonghoon Ko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ko, Gyeonghoon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137533712","display_name":"Juho Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Juho","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":0.40470001101493835,"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":0.40470001101493835,"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":0.1664000004529953,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.08630000054836273,"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/heat-equation","display_name":"Heat equation","score":0.8090000152587891},{"id":"https://openalex.org/keywords/heat-kernel","display_name":"Heat kernel","score":0.7509999871253967},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6916000247001648},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5580999851226807},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5005999803543091},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.47099998593330383},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.44769999384880066},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4408000111579895}],"concepts":[{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.8090000152587891},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.7509999871253967},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6916000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5918999910354614},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5580999851226807},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4733000099658966},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.47099998593330383},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.44769999384880066},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41589999198913574},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4004000127315521},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.32519999146461487},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2928999960422516},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2572999894618988}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.31106","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31106","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,"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.2605.31106","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31106","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,"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Riemannian":[0],"diffusion":[1,12],"models":[2],"generalize":[3],"score-based":[4],"generative":[5],"modeling":[6],"to":[7,90],"manifold-supported":[8],"data":[9],"via":[10],"stochastic":[11],"equations":[13],"on":[14,116],"the":[15,24,48,54,75,92,114],"manifold.":[16],"However,":[17],"training":[18],"requires":[19],"sampling":[20],"from":[21],"and":[22,80,85,105,123],"differentiating":[23],"manifold":[25,55,67],"heat":[26,49,56,77,94],"kernel,":[27],"which":[28],"is":[29],"rarely":[30],"available":[31],"in":[32],"closed":[33],"form":[34],"beyond":[35],"a":[36,43,59,71,81,88],"few":[37],"highly":[38],"symmetric":[39],"manifolds.":[40],"We":[41,112],"propose":[42],"general":[44],"approach":[45],"that":[46],"approximates":[47],"kernel":[50],"by":[51],"directly":[52],"solving":[53],"equation":[57,79],"with":[58],"physics-informed":[60],"neural":[61],"network":[62],"(PINN).":[63],"Given":[64],"an":[65],"explicit":[66],"specification,":[68],"we":[69],"choose":[70],"coordinate":[72],"system,":[73],"derive":[74],"corresponding":[76],"(Fokker--Planck)":[78],"short-time":[82],"asymptotic":[83],"approximation,":[84],"then":[86],"train":[87],"PINN":[89],"learn":[91],"log":[93],"kernel.":[95],"The":[96],"resulting":[97],"surrogate":[98],"enables":[99],"both":[100],"forward":[101],"noising":[102],"(heat-kernel":[103],"sampling)":[104],"conditional-score":[106],"evaluation":[107],"for":[108],"denoising":[109],"score":[110],"matching.":[111],"demonstrate":[113],"method":[115],"diverse":[117],"manifolds":[118],"including":[119],"$S^2$,":[120],"$SO(3)$,":[121],"$\\mathrm{SPD}(n)$,":[122],"permutation-quotiented":[124],"point":[125],"clouds.":[126]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-02T00:00:00"}
