{"id":"https://openalex.org/W7131072766","doi":"https://doi.org/10.48550/arxiv.2602.17706","title":"Parallel Complex Diffusion for Scalable Time Series Generation","display_name":"Parallel Complex Diffusion for Scalable Time Series Generation","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7131072766","doi":"https://doi.org/10.48550/arxiv.2602.17706"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.17706","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121138040","display_name":"Rongyao Cai","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cai, Rongyao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126655798","display_name":"Yuxi Wan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wan, Yuxi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126659155","display_name":"Kexin Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Kexin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126598192","display_name":"Ming Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Ming","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126619994","display_name":"Zhiqiang Ge","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ge, Zhiqiang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126608089","display_name":"Qingsong Wen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen, Qingsong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126598548","display_name":"Yong Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Yong","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5121138040"],"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":0.5806999802589417,"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":0.5806999802589417,"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":0.04989999905228615,"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":0.04230000078678131,"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/series","display_name":"Series (stratigraphy)","score":0.4453999996185303},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.39070001244544983},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.3896999955177307},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.3889999985694885},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.36410000920295715},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.3564999997615814},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.3450999855995178},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.33219999074935913},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.3255000114440918},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.32409998774528503}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5522000193595886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5217999815940857},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.39070001244544983},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.36410000920295715},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.3564999997615814},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35370001196861267},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.3450999855995178},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3181000053882599},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.303600013256073},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.2937999963760376},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C114996537","wikidata":"https://www.wikidata.org/wiki/Q4854529","display_name":"Colors of noise","level":3,"score":0.27639999985694885},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.17706","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.17706","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.17706","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.17706","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":{"Modeling":[0],"long-range":[1],"dependencies":[2],"in":[3,49,171,202],"time":[4,218],"series":[5,219],"generation":[6,204],"poses":[7],"a":[8,42,64,116,168,180,210],"fundamental":[9],"trade-off":[10],"between":[11,108],"representational":[12],"capacity":[13],"and":[14,25,84,101,112,206,213],"computational":[15],"efficiency.":[16],"Traditional":[17],"temporal":[18,70],"diffusion":[19,93],"models":[20],"suffer":[21],"from":[22],"local":[23],"entanglement":[24],"the":[26,50,56,59,80,91,106,140,145,154,162,186,191],"$\\mathcal{O}(L^2)$":[27],"cost":[28],"of":[29,157],"attention":[30,172],"mechanisms.":[31],"We":[32,104,177],"address":[33],"these":[34],"limitations":[35],"by":[36,123,165],"introducing":[37],"PaCoDi":[38,53,152,198],"(Parallel":[39],"Complex":[40],"Diffusion),":[41],"spectral-native":[43],"architecture":[44],"that":[45,90,197],"decouples":[46],"generative":[47],"modeling":[48],"frequency":[51],"domain.":[52],"fundamentally":[54],"alters":[55],"problem":[57],"topology:":[58],"Fourier":[60],"Transform":[61],"acts":[62],"as":[63],"diagonalizing":[65],"operator,":[66],"converting":[67],"locally":[68],"coupled":[69],"signals":[71,159],"into":[72,98],"globally":[73],"decorrelated":[74],"spectral":[75,147],"components.":[76],"Theoretically,":[77],"we":[78,129],"prove":[79],"Quadrature":[81],"Forward":[82],"Diffusion":[83],"Conditional":[85],"Reverse":[86],"Factorization":[87],"theorem,":[88],"demonstrating":[89],"complex":[92],"process":[94],"can":[95],"be":[96],"split":[97],"independent":[99],"real":[100],"imaginary":[102],"branches.":[103],"bridge":[105],"gap":[107],"this":[109,131],"decoupled":[110],"theory":[111],"data":[113],"reality":[114],"using":[115],"\\textbf{Mean":[117],"Field":[118],"Theory":[119],"(MFT)":[120],"approximation}":[121],"reinforced":[122],"an":[124],"interactive":[125],"correction":[126],"mechanism.":[127],"Furthermore,":[128],"generalize":[130],"discrete":[132],"DDPM":[133],"to":[134,160,184],"continuous-time":[135],"Frequency":[136],"SDEs,":[137],"rigorously":[138],"deriving":[139],"Spectral":[141],"Wiener":[142],"Process":[143],"describe":[144],"differential":[146],"Brownian":[148],"motion":[149],"limit.":[150],"Crucially,":[151],"exploits":[153],"Hermitian":[155],"Symmetry":[156],"real-valued":[158],"compress":[161],"sequence":[163],"length":[164],"half,":[166],"achieving":[167],"50%":[169],"reduction":[170],"FLOPs":[173],"without":[174],"information":[175],"loss.":[176],"further":[178],"derive":[179],"rigorous":[181],"Heteroscedastic":[182],"Loss":[183],"handle":[185],"non-isotropic":[187],"noise":[188],"distribution":[189],"on":[190],"compressed":[192],"manifold.":[193],"Extensive":[194],"experiments":[195],"show":[196],"outperforms":[199],"existing":[200],"baselines":[201],"both":[203],"quality":[205],"inference":[207],"speed,":[208],"offering":[209],"theoretically":[211],"grounded":[212],"computationally":[214],"efficient":[215],"solution":[216],"for":[217],"modeling.":[220]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-24T00:00:00"}
