{"id":"https://openalex.org/W7148675458","doi":"https://doi.org/10.48550/arxiv.2604.02250","title":"Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives","display_name":"Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives","publication_year":2026,"publication_date":"2026-04-02","ids":{"openalex":"https://openalex.org/W7148675458","doi":"https://doi.org/10.48550/arxiv.2604.02250"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02250","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02250","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.02250","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132846221","display_name":"Hao Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132918779","display_name":"Di Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Di","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074883462","display_name":"Donna K. Slonim","orcid":"https://orcid.org/0000-0003-3357-437X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Slonim, Donna","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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9879000186920166,"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"}},"topics":[{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9879000186920166,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.00139999995008111,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.0010999999940395355,"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/stability","display_name":"Stability (learning theory)","score":0.6072999835014343},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5550000071525574},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.5041000247001648},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.44859999418258667},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4440999925136566},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.43309998512268066},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.43059998750686646},{"id":"https://openalex.org/keywords/pruning","display_name":"Pruning","score":0.41179999709129333},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4025999903678894},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.38989999890327454}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6093999743461609},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6072999835014343},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5550000071525574},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4986000061035156},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.44859999418258667},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.43059998750686646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42170000076293945},{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41100001335144043},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3118000030517578},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2849999964237213},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2799000144004822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2791000008583069},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.2777000069618225},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02250","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02250","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.02250","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02250","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":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7848069667816162}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"causal":[1,111],"dependencies":[2],"in":[3,39],"observational":[4],"data":[5],"is":[6,45,147],"critical":[7],"for":[8,65],"informing":[9],"decision-making.":[10],"These":[11],"relationships":[12],"are":[13,135],"often":[14,32],"modeled":[15],"as":[16,28],"Bayesian":[17],"Networks":[18],"(BNs)":[19],"and":[20,30,37],"Directed":[21],"Acyclic":[22],"Graphs":[23],"(DAGs).":[24],"Existing":[25],"methods,":[26],"such":[27],"NOTEARS":[29],"DAG-GNN,":[31],"face":[33],"issues":[34],"with":[35],"scalability":[36],"stability":[38],"high-dimensional":[40],"data,":[41],"especially":[42],"when":[43],"there":[44],"a":[46,109],"feature-sample":[47],"imbalance.":[48],"Here,":[49],"we":[50],"show":[51,131],"that":[52,78,84,132],"the":[53,63,103,120],"denoising":[54,105],"score":[55],"matching":[56],"objective":[57],"of":[58,123],"diffusion":[59,99],"models":[60],"could":[61],"smooth":[62],"gradients":[64],"faster,":[66],"more":[67],"stable":[68],"convergence.":[69],"We":[70,88,118,129],"also":[71,130],"propose":[72],"an":[73],"adaptive":[74],"k-hop":[75],"acyclicity":[76],"constraint":[77],"improves":[79],"runtime":[80],"over":[81],"existing":[82],"solutions":[83],"require":[85],"matrix":[86],"inversion.":[87],"name":[89],"this":[90,150],"framework":[91],"Denoising":[92],"Diffusion":[93],"Causal":[94],"Discovery":[95],"(DDCD).":[96],"Unlike":[97],"generative":[98],"models,":[100],"DDCD":[101],"utilizes":[102],"reverse":[104],"process":[106],"to":[107,115],"infer":[108],"parameterized":[110],"structure":[112],"rather":[113],"than":[114],"generate":[116],"data.":[117,128],"demonstrate":[119],"competitive":[121],"performance":[122],"DDCDs":[124],"on":[125,142],"synthetic":[126],"benchmarking":[127],"our":[133],"methods":[134],"practically":[136],"useful":[137],"by":[138],"conducting":[139],"qualitative":[140],"analyses":[141],"two":[143],"real-world":[144],"examples.":[145],"Code":[146],"available":[148],"at":[149],"url:":[151],"https://github.com/haozhu233/ddcd.":[152]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-04T00:00:00"}