{"paper":{"title":"Follow the Mean: Reference-Guided Flow Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Flow matching admits controllable generation by shifting the conditional endpoint mean computed from a reference set, enabling training-free guidance on frozen pretrained models.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Floor Eijkelboom, Jan-Willem van de Meent, Maksim Zhdanov, Pedro M. P. Curvo","submitted_at":"2026-05-11T09:57:34Z","abstract_excerpt":"Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the interpolants remain deterministic and that the endpoint mean fully determines the velocity field without additional dependencies on the reference distribution or noise schedule.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Flow matching admits controllable generation by shifting the conditional endpoint mean computed from a reference set, enabling training-free guidance on frozen pretrained models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"78bce1303f961d9f94e19a430e91abc5c8f32eb642002fad583b0b5332de6958"},"source":{"id":"2605.10302","kind":"arxiv","version":3},"verdict":{"id":"acecccaf-d52c-4593-abeb-2497743dc524","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T06:10:13.891989Z","strongest_claim":"For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself.","one_line_summary":"Flow matching admits controllable generation by shifting the conditional endpoint mean computed from a reference set, enabling training-free guidance on frozen pretrained models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the interpolants remain deterministic and that the endpoint mean fully determines the velocity field without additional dependencies on the reference distribution or noise schedule.","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.10302/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T06:02:01.221587Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T15:36:43.287558Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T11:31:19.101354Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T09:28:50.477382Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"eafd757ab53e195c3de051808644a24ce1b58de3a95e4b22809c900f2745d650"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4a58e42964c11cf471b77c7df0bc4e113b2f50cffdc91bc46456b3f7455f59aa"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}