{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:46AJFWUMFLTBNW3DVWT6ADUIBO","short_pith_number":"pith:46AJFWUM","schema_version":"1.0","canonical_sha256":"e78092da8c2ae616db63ada7e00e880b8d9dd9ce6769522a8f0984f4ffdee077","source":{"kind":"arxiv","id":"2412.18730","version":4},"attestation_state":"computed","paper":{"title":"Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries and Denoisers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Gal Mishne, Qingsong Wang, Yusu Wang, Zhengchao Wan","submitted_at":"2024-12-25T01:17:15Z","abstract_excerpt":"Flow matching (FM) models extend ODE sampler based diffusion models into a general framework, significantly reducing sampling steps through learned vector fields. However, the theoretical understanding of FM models, particularly how their sample trajectories interact with underlying data geometry, remains underexplored. A rigorous theoretical analysis of FM ODE is essential for sample quality, stability, and broader applicability. In this paper, we advance the theory of FM models through a comprehensive analysis of sample trajectories. Central to our theory is the discovery that the denoiser, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.18730","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-25T01:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"a5361283f2a80a6ce5f69ac28859b4b127d5556c828c0aa1364711ad539a0bb3","abstract_canon_sha256":"25810a332dc1b30b795438cc9c9bdce16bbe20b7e09a82bdcce43a66fdd5a75a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:26.294966Z","signature_b64":"yp2Vt6mW6SRK941hYpaoqCuh3W4kj2aNZ4YSrFNq5Eh9/tlsZn+syM9ru/iLoAdi0iv7Rw5Fwy56nm76VveOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e78092da8c2ae616db63ada7e00e880b8d9dd9ce6769522a8f0984f4ffdee077","last_reissued_at":"2026-07-05T11:14:26.294389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:26.294389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries and Denoisers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Gal Mishne, Qingsong Wang, Yusu Wang, Zhengchao Wan","submitted_at":"2024-12-25T01:17:15Z","abstract_excerpt":"Flow matching (FM) models extend ODE sampler based diffusion models into a general framework, significantly reducing sampling steps through learned vector fields. However, the theoretical understanding of FM models, particularly how their sample trajectories interact with underlying data geometry, remains underexplored. A rigorous theoretical analysis of FM ODE is essential for sample quality, stability, and broader applicability. In this paper, we advance the theory of FM models through a comprehensive analysis of sample trajectories. Central to our theory is the discovery that the denoiser, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18730","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18730/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.18730","created_at":"2026-07-05T11:14:26.294467+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.18730v4","created_at":"2026-07-05T11:14:26.294467+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18730","created_at":"2026-07-05T11:14:26.294467+00:00"},{"alias_kind":"pith_short_12","alias_value":"46AJFWUMFLTB","created_at":"2026-07-05T11:14:26.294467+00:00"},{"alias_kind":"pith_short_16","alias_value":"46AJFWUMFLTBNW3D","created_at":"2026-07-05T11:14:26.294467+00:00"},{"alias_kind":"pith_short_8","alias_value":"46AJFWUM","created_at":"2026-07-05T11:14:26.294467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.15785","citing_title":"Memorization and Regularization in Generative Diffusion Models","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO","json":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO.json","graph_json":"https://pith.science/api/pith-number/46AJFWUMFLTBNW3DVWT6ADUIBO/graph.json","events_json":"https://pith.science/api/pith-number/46AJFWUMFLTBNW3DVWT6ADUIBO/events.json","paper":"https://pith.science/paper/46AJFWUM"},"agent_actions":{"view_html":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO","download_json":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO.json","view_paper":"https://pith.science/paper/46AJFWUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.18730&json=true","fetch_graph":"https://pith.science/api/pith-number/46AJFWUMFLTBNW3DVWT6ADUIBO/graph.json","fetch_events":"https://pith.science/api/pith-number/46AJFWUMFLTBNW3DVWT6ADUIBO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO/action/storage_attestation","attest_author":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO/action/author_attestation","sign_citation":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO/action/citation_signature","submit_replication":"https://pith.science/pith/46AJFWUMFLTBNW3DVWT6ADUIBO/action/replication_record"}},"created_at":"2026-07-05T11:14:26.294467+00:00","updated_at":"2026-07-05T11:14:26.294467+00:00"}