[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83527-en":3,"doc-seo-83527-105":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},83527,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Self-conditioned Flow Map Language Models via Fixed-point Flows","Self-conditioning improves continuous-flow language models by denoising generated text conditioned on the model’s own denoising estimate, yet the source of gains is insufficiently explained. It is also unclear how to use self-conditioning for few-step generators based on flow maps. This work shows that self-conditioned flow language models solve a fixed-point iteration that bootstraps the learned denoiser. It introduces fixed-point flows and distills them into valid flow maps, yielding FMLM⋆ with state-of-the-art one- and few-step generation on OpenWebText.","arXiv :2607 .007 14v 1 [ cs .CL] 1 Jul 2026  \nSELF-CONDITIONED FLOW MAP LANGUAGE MODELS VIA FIXED-POINT FLOWS  \nJaehoon Yoo 1 ∗ Wonjung Kim 1 ∗ Floor Eijkelboom2 Chanhyuk Lee 1 Nicholas M. Boffi3 Seunghoon Hong 1† Jinwoo Kim 1†  \n1 KAIST 2University of Amsterdam 3 Carnegie Mellon University  \nABSTRACT  \nSelf-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning solve a fixed-point iteration that bootstraps the performance of the learned denoiser. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of selfconditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM⋆ , outperforms state-of-the-art self-conditioned models and few-step models in one-and few-step generation on OpenWebText.1  \n1 INTRODUCTION  \nLanguage models (LMs) based on continuous flows have recently emerged as a promising paradigm for non-autoregressive text generation (Lee et al., 2026 ; Chemseddine et al., 2026 ; Deschenaux & Gulcehre, 2026) . By learning to denoise tokens in a continuous space, these models perform parallel iterative generation through a deterministic evolution driven by a velocity field. Importantly, such processes define a unique flow map, the solution operator that directly transports noise to data in as few as one function evaluation. This advantage has sparked recent breakthroughs on distillation offlow language models into flow map language models that are capable of generating text in one to few inference steps (Lee et al., 2026 ; Roos et al., 2026 ; Potaptchik et al., 2026) .  \nRecently, the performance of flow language models has improved through the incorporation of a self-conditioning mechanism (Chen et al., 2022) . Unlike in usual flow training, self-conditioned flow models learn to denoise an input by conditioning on its own denoising prediction. Then, during generation, they perform denoising at each flow timestep by conditioning on the previously denoised outcome. Self-conditioning has empirically proven very effective (Dieleman et al., 2022 ; Strudel et al., 2022), and has been widely adopted in the latest state-of-the-art flow language models (Chenet al., 2026 ; Hu et al., 2026 ; Batzolis et al., 2026 ; Meshchaninov et al., 2026 ; Yang et al., 2026) . Yet, despite its success, why self-conditioning leads to improvements remains poorly understood. Furthermore, it is unclear how to distill flows into flow maps under self-conditioning, as it introduces additional dependencies across generation timesteps.  \nIn this work, we introduce fixed-point flows, a mathematical framework for self-conditioned flows and their associated flow maps (Figure 1) . Our key observation is that self-conditioned flow language models solve a fixed-point iteration that bootstraps the performance of learned denoising. With this insight, we characterize a two-dimensional class of self-conditioned flows, where the first dimension represents the original flow, and the second represents fixed-point iterations. We use this view to distill self-conditioned flow language models into flow maps by compressing both fixed-point iterations and flow, achieving state-of-the-art one-and few-step language modeling. Our main contributions are:  \n∗Equal contr","cbCaiibDF8zAwiPT","https://ap.wps.com/l/cbCaiibDF8zAwiPT","pdf",581610,4,1,25,"English","en",105,"# Abstract\n# Introduction\n# Preliminary","[{\"question\":\"What problem does self-conditioning address in flow-based language models?\",\"answer\":\"Self-conditioning enhances continuous-flow language models by denoising generated text while conditioning on the model’s own prior denoising estimate during generation timesteps.\"},{\"question\":\"How does this paper explain why self-conditioning improves performance?\",\"answer\":\"The paper shows self-conditioned flow language models implicitly solve a fixed-point iteration that bootstraps the performance of the learned denoiser.\"},{\"question\":\"What are fixed-point flows and how do they lead to flow map language models?\",\"answer\":\"Fixed-point flows are a two-dimensional class of self-conditioned flows where one dimension runs the flow process and the other runs fixed-point iteration. The resulting framework yields valid flow maps that can be distilled from self-conditioned flow models, producing a one- and few-step generator (FMLM⋆).\"}]",1784188626,63,{"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},"self-conditioned-flow-map-language-models-via-fixed-point-flows","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/self-conditioned-flow-map-language-models-via-fixed-point-flows/83527/",{"url":52,"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","2026-07-26","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},"What problem does self-conditioning address in flow-based language models?","Question",{"text":75,"@type":76},"Self-conditioning enhances continuous-flow language models by denoising generated text while conditioning on the model’s own prior denoising estimate during generation timesteps.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does this paper explain why self-conditioning improves performance?",{"text":80,"@type":76},"The paper shows self-conditioned flow language models implicitly solve a fixed-point iteration that bootstraps the performance of the learned denoiser.",{"name":82,"@type":73,"acceptedAnswer":83},"What are fixed-point flows and how do they lead to flow map language models?",{"text":84,"@type":76},"Fixed-point flows are a two-dimensional class of self-conditioned flows where one dimension runs the flow process and the other runs fixed-point iteration. The resulting framework yields valid flow maps that can be distilled from self-conditioned flow models, producing a one- and few-step generator (FMLM⋆).","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"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":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"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"]