[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85847-en":3,"doc-seo-85847-105":30,"detail-sidebar-cat-0-en-105":92},{"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},85847,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Source Lifted Flow Matching for Intervenable Multimodal Imitation","Flow-matching policies are effective for imitation learning by modeling complex multimodal action distributions, yet their randomness is largely passive: sampling varies outcomes but users cannot choose among valid future continuations from the same state. Source-Lifted Flow Matching (SL-FM) introduces a source-intervenable handle while keeping a shared, latent-free velocity field. Orthogonal Source Lifting prevents path-crossing identity ambiguity, enabling action-branch selection via source geometry. End-to-end learning with a state-dependent source mixture and responsibility floor improves usability across states. Experiments show improved robot control performance and fewer crossing-induced composite trajectories.","Source-Lifted Flow Matching for Intervenable Multimodal Imitation  \nHe Zhang1 , Ying Sun1∗, Pengteng Li1 , Ziyang Chen1 , Yiren Zhao1 , Ziyang Rao1 , Weiyu Guo1 , Yandong Guo2 , Hui Xiong1∗  \n1The Hong Kong University of Science and Technology (Guangzhou)  \n2AI2 Robotics  \narXiv :2607 . 10206v1 [ cs .RO] 11 Jul 2026  \nAbstract  \nFlow-matching policies are promising for imitation learning because they model complex multimodal action distributions. However, their stochasticity is largely passive: repeated sampling may yield diverse behaviors, but users cannot directly choose among valid continuations from the same state. We propose Source-Lifted Flow Matching (SL-FM), a sourceintervenable flow-matching policy that exposes such a handle while keeping the velocity field shared and latent-free. The handle selects only the source endpoint of the conditional flow, not a mode-specific field, preserving the standard formulation while avoiding decomposition into separate modeconditioned dynamics. The core mechanism is Orthogonal Source Lifting, designed to prevent path-crossing ambiguity. Instead of partitioning target actions by mode, SL-FM lifts handle-specific sources into auxiliary orthogonal coordinates and keeps targets in the original action subspace. This preserves the demonstrated action distribution while allowing one shared field to carry different branches without merging at crossings. To keep handles usable across states, we learn a state-dependent source mixture end to end and use a responsibility floor, giving each handle weak supervision and mitigating dead modes. Experiments on crossing-flow diagnostics and robot-control benchmarks show that SL-FM converts passive source randomness into an actionable intervention variable. It removes crossing-induced composite trajectories, changes future routes in 91.1% of matched-prefix interventions, and achieves strong free-deployment performance, with improvements in several benchmark settings. Overall, source geometry provides actionable multimodal control without conditioning the velocity field on the selected mode.  \nIntroduction  \nRecent advances in imitation learning have increasingly leveraged generative policies to model complex, multimodal action distributions (Chi et al. 2023; Pearce et al. 2023; Jiang et al. 2025) . Unlike conventional behavioral cloning methods that often assume a unimodal Gaussian policy (Florence et al. 2022; Shafiullah et al. 2022), diffusion and flow-matching policies can represent multiple plausible actions for the same observation (Chi et al. 2023; Lipman et al. 2023; Jiang et al. 2025), which is essential in robot tasks with several valid strategies (Jia et al. 2024; Chi et al. 2023) . For example, in obstacle avoidance, demonstrations may pass an obstacle from either side; a good policy should preserve both alternatives rather than collapse them into an averaged action.  \n∗Corresponding author.  \nFigure 1: Main idea of Source-Lifted Flow Matching. Standard flow matching passively samples multimodal behaviors, while mode-conditioned fields may split both the target distribution and velocity field.. SL-FM instead lifts handle-specific sources into orthogonal coordinates, keeps all targets in the original action subspace, and uses one shared latent-free field to preserve source identity through crossings.  \nHowever, representing diverse behaviors is not the same as controlling them. Existing flow-matching policies usually use source noise as a passive sampling mechanism (Lipman et al. 2023; Jiang et al. 2025): resampling the source may produce different rollouts, but the user cannot directly choose which continuation will be realized from a fixed decision state. This distinction matters for downstream planning, human-in-theloop control, and robot tasks where several valid futures share the same prefix. A policy that sometimes goes left and sometimes goes right is useful; one that lets a planner choose the continuation from the same local state is mo","cbCair0PtlOOd9rp","https://ap.wps.com/l/cbCair0PtlOOd9rp","pdf",2409199,5,1,11,"English","en",105,"# Introduction\n## Motivation: passive multimodality vs controllable futures\n## Limitation of mode-conditioned approaches\n## Proposed method: Source-Lifted Flow Matching (SL-FM)\n## Key challenge: source identity at crossings\n## Orthogonal Source Lifting","[{\"question\":\"What problem does Source-Lifted Flow Matching (SL-FM) address in imitation learning?\",\"answer\":\"SL-FM addresses the gap between generating diverse multimodal actions and giving users/planners the ability to select a desired continuation from the same decision state.\"},{\"question\":\"How does SL-FM let a user intervene to choose among multimodal futures?\",\"answer\":\"SL-FM assigns each state source handles that can be sampled from a learned prior or set externally at test time. The handle determines only the start of the conditional flow, not the velocity field dynamics.\"},{\"question\":\"Why is Orthogonal Source Lifting important in SL-FM?\",\"answer\":\"Orthogonal Source Lifting prevents path-crossing ambiguity where a shared field could mix incompatible velocities. It lifts handle-specific sources into auxiliary orthogonal coordinates while keeping target actions in the original action space.\"}]",1784206682,28,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"source-lifted-flow-matching-for-intervenable-multimodal-imitation","",{"@graph":36,"@context":86},[37,54,69],{"@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":53},"https://docshare.wps.com/document/source-lifted-flow-matching-for-intervenable-multimodal-imitation/85847/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does Source-Lifted Flow Matching (SL-FM) address in imitation learning?","Question",{"text":76,"@type":77},"SL-FM addresses the gap between generating diverse multimodal actions and giving users/planners the ability to select a desired continuation from the same decision state.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does SL-FM let a user intervene to choose among multimodal futures?",{"text":81,"@type":77},"SL-FM assigns each state source handles that can be sampled from a learned prior or set externally at test time. The handle determines only the start of the conditional flow, not the velocity field dynamics.",{"name":83,"@type":74,"acceptedAnswer":84},"Why is Orthogonal Source Lifting important in SL-FM?",{"text":85,"@type":77},"Orthogonal Source Lifting prevents path-crossing ambiguity where a shared field could mix incompatible velocities. It lifts handle-specific sources into auxiliary orthogonal coordinates while keeping target actions in the original action space.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"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":20,"slug":138},19,"General","general"]