{"id":"https://openalex.org/W7155000796","doi":"https://doi.org/10.48550/arxiv.2604.15694","title":"Neural Continuous-Time Markov Chain: Discrete Diffusion via Decoupled Jump Timing and Direction","display_name":"Neural Continuous-Time Markov Chain: Discrete Diffusion via Decoupled Jump Timing and Direction","publication_year":2026,"publication_date":"2026-04-17","ids":{"openalex":"https://openalex.org/W7155000796","doi":"https://doi.org/10.48550/arxiv.2604.15694"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.15694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15694","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.15694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035060797","display_name":"Jingyuan Li","orcid":"https://orcid.org/0000-0002-4434-2673"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Jingyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134015564","display_name":"Xiaoyi Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Xiaoyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134037679","display_name":"Fukang Wen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen, Fukang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100431658","display_name":"Wei Liu","orcid":"https://orcid.org/0000-0001-7118-815X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030131487","display_name":"Renqian Luo","orcid":"https://orcid.org/0000-0002-9062-3484"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Renqian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134054958","display_name":"Yi Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134016284","display_name":"Zuoqiang Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Zuoqiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073715806","display_name":"Pipi Hu","orcid":"https://orcid.org/0000-0001-8129-0027"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Pipi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5035060797"],"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":0.5311999917030334,"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":0.5311999917030334,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0746999979019165,"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"}},{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.06400000303983688,"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/jump","display_name":"Jump","score":0.630299985408783},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5722000002861023},{"id":"https://openalex.org/keywords/jump-process","display_name":"Jump process","score":0.5559999942779541},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5555999875068665},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5263000130653381},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.47350001335144043},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.45590001344680786},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.423799991607666},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.414000004529953},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4059999883174896}],"concepts":[{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.630299985408783},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5722000002861023},{"id":"https://openalex.org/C2776825372","wikidata":"https://www.wikidata.org/wiki/Q3922411","display_name":"Jump process","level":3,"score":0.5559999942779541},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5555999875068665},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5263000130653381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5213000178337097},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42980000376701355},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.414000004529953},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4050999879837036},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38839998841285706},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37070000171661377},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35679998993873596},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C2779664328","wikidata":"https://www.wikidata.org/wiki/Q6311158","display_name":"Jump diffusion","level":3,"score":0.34700000286102295},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.31520000100135803},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C70557757","wikidata":"https://www.wikidata.org/wiki/Q7834432","display_name":"Transition rate matrix","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2676999866962433},{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.2540999948978424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.15694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15694","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":"doi:10.48550/arxiv.2604.15694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.15694","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":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":{"Discrete":[0],"diffusion":[1],"models":[2],"based":[3],"on":[4,13,152],"continuous-time":[5],"Markov":[6],"chains":[7],"(CTMCs)":[8],"have":[9],"shown":[10],"strong":[11],"performance":[12],"language":[14],"and":[15,56,85,114,126,132,137,157,191],"discrete":[16],"data":[17],"generation,":[18],"yet":[19],"existing":[20],"approaches":[21],"typically":[22],"parameterize":[23],"the":[24,46,49,65,75,100,112,164,168,177],"reverse":[25,76,116],"rate":[26],"matrix":[27],"monolithically":[28],"--":[29,42],"through":[30,78],"proxies":[31],"such":[32],"as":[33],"concrete":[34],"scores":[35],"(SEDD)":[36],"or":[37],"clean-data":[38],"predictions":[39],"(MDLM,":[40],"GIDD)":[41],"rather":[43],"than":[44],"aligning":[45],"parameterization":[47],"with":[48],"intrinsic":[50],"CTMC":[51,70,147,186],"decomposition":[52],"into":[53,120],"jump":[54,57],"timing":[55,125],"direction.":[58],"We":[59,97],"propose":[60],"\\textbf{Neural":[61],"CTMC},":[62],"which":[63],"exploits":[64],"underlying":[66],"Poisson":[67,122],"structure":[68],"of":[69],"dynamics":[71],"by":[72,142],"separately":[73],"parameterizing":[74],"process":[77],"an":[79],"\\emph{exit":[80],"rate}":[81],"(when":[82],"to":[83,90,106],"jump)":[84,91],"a":[86,107,121,127,134],"\\emph{jump":[87],"distribution}":[88],"(where":[89],"via":[92],"two":[93],"dedicated":[94],"network":[95],"heads.":[96],"show":[98],"that":[99,118],"evidence":[101],"lower":[102],"bound":[103],"(ELBO)":[104],"reduces":[105],"path-space":[108],"KL":[109,123,129],"divergence":[110],"between":[111],"true":[113],"learned":[115],"processes":[117],"factorizes":[119],"for":[124,130],"categorical":[128],"direction,":[131],"admits":[133],"tractable,":[135],"gradient-equivalent":[136],"consistent":[138],"loss.":[139],"Experimentally,":[140],"scored":[141],"Gemma2-9B,":[143],"our":[144,199],"pure-uniform":[145],"Neural":[146,185],"achieves":[148],"$16.36$":[149],"generative":[150],"perplexity":[151,166],"TinyStories":[153],"(vs.\\":[154],"GIDD":[155,192],"$37.60$":[156],"MDLM":[158,189],"$42.66$).":[159],"On":[160],"OpenWebText,":[161],"it":[162],"attains":[163],"best":[165],"at":[167,182,202],"same":[169],"training-token":[170],"budget":[171],"across":[172],"16--128":[173],"sampling":[174],"steps":[175],"among":[176],"methods":[178],"we":[179,197],"compare":[180],"(e.g.,":[181],"128":[183],"steps:":[184],"$183.6$":[187],"vs.\\":[188],"$210.5$":[190],"$249.8$).":[193],"To":[194],"facilitate":[195],"reproducibility,":[196],"release":[198],"pretrained":[200],"weights":[201],"https://huggingface.co/Jiangxy1117/Neural-CTMC.":[203]},"counts_by_year":[],"updated_date":"2026-05-12T06:07:45.972803","created_date":"2026-04-21T00:00:00"}