[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82161-en":3,"doc-seo-82161-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82161,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Variable-Length Generative Protein Design via Generalized Poisson Flow","The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to designability. Current diffusion- and flow-based generative models typically require a pre-specified protein length before sampling, limiting exploration of feasible designs. Generalized Poisson Flow (GPFlow) introduces a variable-length generative framework that learns an inhomogeneous generalized Poisson rate function via negative log-likelihood training, with population-level and KL-divergence recovery guarantees. Evaluations cover structure/sequence design, motif scaffolding, and peptide co-design across multiple modalities, confirming strong variable-length generation quality.","Variable-Length Generative Protein Design via Generalized Poisson Flow  \nChaoran Cheng∗ , Zhanghan Ni∗ , Yanru Qu∗ , Yuxin Chen, Ruihan Guo, Jiajun Fan, Ge Liu  \nSiebel School of Computing and Data Science  \nUniversity of Illinois Urbana-Champaign  \narXiv :2607 .09039v 1 [ cs .LG] 10 Jul 2026  \n(a) Unconditional Structure Design  \n(b) Unconditional Sequence Design  \nAPSQDTALWKGELTYGDVPDITEYSG PDTEYVGMSNAT  \nDAPSQIVKDVTDTALIWF KLEDGELTYGDVPGDRTT ITDEQYSIGNLKPDTEYE VSLRRGDMSSNAKETT  \nLDAPSQIEVKDVTDTTALITWFK PLAEIDGIELTYGIKDVPGDRTT IDLTEDENQYSIGNLKPDTEYEVSLISRRGDMSSNPAKETFTT  \n(c) Conditional Structure-Based Motif-Scaffolding (d) Conditional Sequence-based Motif-Scaffolding  \nLPEYYGENLDALWDALTGWVEY  \nDTLKKELALPEYYGENLDALWDALTGWVEYPLVLEWRQFS  \nMKKAVINGEQIRSISDLHQ TLKKELALPEYYGENLDAL WDALTGWVEYPLVLEWRQFEQSKQLTENGAESLQVFA  \nMKKAVINGEQIRSISDLHQTLKKELALPEYYGENLDALWDALTGWVEYPLVLEWRQFEQSKQLTENGAESVLQVFREAKAEGADITIILS  \n(e) Conditional Peptide Structure-Sequence Co-Design  \n QTKA  \nQLAT  \nKAAK  \nQLATKAAR  KSAPATG  \n(a) 96.1% vs 77.6% Designability↑  \n(b) 3.17 vs 14.40 ΔpLDDT↓  \n(c) 10 vs 3 Top-1 unique success↑  \n(d) 10 vs 6 Passed tasks↑  \n(e) 1.35 Å vs 1.99 Å RMSD↓  \n(Proteina)(DPLM)(Proteina)(DPLM)(PepFlow)  \nAbstract  \nThe ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to designability. Current diffusion-and flow-based generative models typically require the protein length to be specified before sampling, limiting their flexibility in exploring the feasible design space. To address this limitation, we introduce Generalized Poisson Flow (GPFlow), a variable-length generative framework that learns the rate function of an inhomogeneous generalized Poisson process by minimizing its negative log-likelihood. We establish population-level guarantees for recovering the joint multimodal distribution and derive an upper bound on the KL divergence between the data and generated distributions. We comprehensively evaluate GPFlow across structure and sequence design, motif scaffolding, and peptide co-design, spanning Euclidean, categorical, and Riemannian modalities to fully validate its variablelength generation quality. In unconditional design, GPFlow improves structural designability and achieves the best distributional fitness for sequence design compared to their corresponding fixed-length baselines, while perfectly recovering the length distribution. In conditional motif scaffolding, GPFlow ranks first on 10 of 16 structure-based design tasks with significantly more unique successes and also achieves more passed tasks in sequence-based design. In peptide co-design, GPFlow remains competitive even without access to a native-length oracle.  \n*Equal contribution.  \nCorrespondence to [chaoran7@illinois.edu](chaoran7@illinois.edu).  \nPreprint.  \n1 Introduction  \nDiffusion models [22, 42] and flow matching [34] have become widely used frameworks for protein generative modeling and have produced strong results in protein design [40, 18, 31] . However, their standard formulations operate on fixed-dimensional state spaces. Such a constraint is restrictive fortasks like motif scaffolding, where the optimal length is often unknown a priori and is tightly coupled to designability. Sampling sweep over a pre-specified length range increases inference cost and may miss feasible designs when the selected lengths are incompatible with the conditional constraints. To bridge this gap, we introduce Generalized Poisson Flow (GPFlow), a variable-length generative framework in which length evolves under an inhomogeneous generalized Poisson process. GPFlow couples this length process to a within-length generator, thereby accommodating continuous, discrete, Riemannian, and mixed length-dependent modalities within the same construction. Building on a marginalization theorem for the conditional process, we derive a tractable objective from the negative log-likelihood (NLL) of the","cbCaiuwFjpQaw4Gs","https://ap.wps.com/l/cbCaiuwFjpQaw4Gs","pdf",6734652,2,1,42,"English","en",105,"# Introduction\n## Five protein design scenarios\n# Variable-length generative framework","[{\"question\":\"为什么固定长度的生成模型不适合某些蛋白设计任务？\",\"answer\":\"固定长度的扩散/流模型需要在采样前指定蛋白长度，这会增加推理成本，并且当所选长度与条件约束不匹配时可能错过可行设计。\"},{\"question\":\"GPFlow如何实现可变长度蛋白生成？\",\"answer\":\"GPFlow让长度在一个非齐次广义泊松过程中演化，并将该长度过程与同长度内部的生成器耦合，从而支持连续、离散以及黎曼等多种长度相关模态。\"},{\"question\":\"GPFlow在不同任务上取得了哪些改进？\",\"answer\":\"在无条件结构设计中提升结构可设计性，并在序列设计上获得最佳分布适配；在条件基序-支架任务中，多数结构任务排名第一且独特成功更多；在肽的结构-序列联合设计中，即使没有原生长度先验仍保持竞争力。\"}]",1784178515,106,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"variable-length-generative-protein-design-via-generalized-poisson-flow","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/variable-length-generative-protein-design-via-generalized-poisson-flow/82161/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-20","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"为什么固定长度的生成模型不适合某些蛋白设计任务？","Question",{"text":75,"@type":76},"固定长度的扩散/流模型需要在采样前指定蛋白长度，这会增加推理成本，并且当所选长度与条件约束不匹配时可能错过可行设计。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"GPFlow如何实现可变长度蛋白生成？",{"text":80,"@type":76},"GPFlow让长度在一个非齐次广义泊松过程中演化，并将该长度过程与同长度内部的生成器耦合，从而支持连续、离散以及黎曼等多种长度相关模态。",{"name":82,"@type":73,"acceptedAnswer":83},"GPFlow在不同任务上取得了哪些改进？",{"text":84,"@type":76},"在无条件结构设计中提升结构可设计性，并在序列设计上获得最佳分布适配；在条件基序-支架任务中，多数结构任务排名第一且独特成功更多；在肽的结构-序列联合设计中，即使没有原生长度先验仍保持竞争力。","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]