{"id":"https://openalex.org/W7138270972","doi":"https://doi.org/10.48550/arxiv.2603.14704","title":"Chain-of-Trajectories: Unlocking the Intrinsic Generative Optimality of Diffusion Models via Graph-Theoretic Planning","display_name":"Chain-of-Trajectories: Unlocking the Intrinsic Generative Optimality of Diffusion Models via Graph-Theoretic Planning","publication_year":2026,"publication_date":"2026-03-16","ids":{"openalex":"https://openalex.org/W7138270972","doi":"https://doi.org/10.48550/arxiv.2603.14704"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.14704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.14704","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.14704","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129726177","display_name":"Ping Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Ping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129714841","display_name":"Xiang Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067983994","display_name":"Xingpeng Zhang","orcid":"https://orcid.org/0000-0001-6547-6374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Xingpeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129733298","display_name":"Fei Shen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Fei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129653061","display_name":"Xun Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Xun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129715619","display_name":"Zhaoxiang Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zhaoxiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129715526","display_name":"Zezhou Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Zezhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129654038","display_name":"Huan Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Huan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129749400","display_name":"Kai Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Kai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129705881","display_name":"Shiguo Lian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lian, Shiguo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5129726177"],"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":0.20679999887943268,"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":0.20679999887943268,"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/T11287","display_name":"Cancer Genomics and Diagnostics","score":0.16500000655651093,"subfield":{"id":"https://openalex.org/subfields/1306","display_name":"Cancer Research"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.0851999968290329,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4957999885082245},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49380001425743103},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4431000053882599},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.3855000138282776},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.38040000200271606},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.37630000710487366},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.36010000109672546},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3463999927043915},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.33160001039505005},{"id":"https://openalex.org/keywords/diffusion-map","display_name":"Diffusion map","score":0.3278999924659729}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5979999899864197},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4957999885082245},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4941999912261963},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41920000314712524},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3783999979496002},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.37630000710487366},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.36010000109672546},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33489999175071716},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.3278999924659729},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3262999951839447},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2906000018119812},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2556000053882599},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.2506999969482422},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.14704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.14704","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.14704","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.14704","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":"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":{"Diffusion":[0,67],"models":[1,119],"operate":[2],"in":[3,32],"a":[4,11,55,69,80,96,101,138],"reflexive":[5],"System":[6,59],"1":[7],"mode,":[8],"constrained":[9],"by":[10],"fixed,":[12],"content-agnostic":[13],"sampling":[14,91],"schedule.":[15],"This":[16,135],"rigidity":[17],"arises":[18],"from":[19],"the":[20,26,33,83,110],"curse":[21],"of":[22,29],"state":[23,85],"dimensionality,":[24],"where":[25],"combinatorial":[27],"explosion":[28],"possible":[30],"states":[31],"high-dimensional":[34,84],"noise":[35],"manifold":[36],"renders":[37],"explicit":[38],"trajectory":[39],"planning":[40,94],"intractable":[41],"and":[42,77,129],"leads":[43],"to":[44,64,89,109],"systematic":[45],"computational":[46,107],"misallocation.":[47],"To":[48],"address":[49],"this,":[50],"we":[51],"introduce":[52],"Chain-of-Trajectories":[53],"(CoTj),":[54],"train-free":[56],"framework":[57],"enabling":[58],"2":[60],"deliberative":[61],"planning.":[62],"Central":[63],"CoTj":[65,104,122],"is":[66,148],"DNA,":[68],"low-dimensional":[70],"signature":[71],"that":[72,121],"quantifies":[73],"per-stage":[74],"denoising":[75],"difficulty":[76],"serves":[78],"as":[79,92],"proxy":[81],"for":[82,141],"space,":[86],"allowing":[87],"us":[88],"reformulate":[90],"graph":[93],"on":[95],"directed":[97],"acyclic":[98],"graph.":[99],"Through":[100],"Predict-Plan-Execute":[102],"paradigm,":[103],"dynamically":[105],"allocates":[106],"effort":[108],"most":[111],"challenging":[112],"generative":[113,118],"phases.":[114],"Experiments":[115],"across":[116],"multiple":[117],"demonstrate":[120],"discovers":[123],"context-aware":[124],"trajectories,":[125],"improving":[126],"output":[127],"quality":[128],"stability":[130],"while":[131],"reducing":[132],"redundant":[133],"computation.":[134],"work":[136],"establishes":[137],"new":[139],"foundation":[140],"resource-aware,":[142],"planning-based":[143],"diffusion":[144],"modeling.":[145],"The":[146],"code":[147],"available":[149],"at":[150],"https://github.com/UnicomAI/CoTj.":[151]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-03-18T00:00:00"}