{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:L7K364KW6A2R23A6F5HFSPVELC","short_pith_number":"pith:L7K364KW","schema_version":"1.0","canonical_sha256":"5fd5bf7156f0351d6c1e2f4e593ea458a5c509f4e491a94ef36d0eb11f44043d","source":{"kind":"arxiv","id":"2602.10989","version":2},"attestation_state":"computed","paper":{"title":"Variational Optimality of F\\\"ollmer Processes in Generative Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Eric Vanden-Eijnden, Yifan Chen","submitted_at":"2026-02-11T16:15:19Z","abstract_excerpt":"We construct and analyze generative diffusions that transport a point mass to a prescribed target distribution over a finite time horizon using the stochastic interpolant framework. The drift is expressed as a conditional expectation that can be estimated from independent samples without simulating stochastic processes. We show that the diffusion coefficient can be tuned \\emph{a~posteriori} without changing the time-marginal distributions. Among all such tunings, we prove that minimizing the impact of estimation error on the path-space Kullback--Leibler divergence selects, in closed form, a F\\"},"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":"2602.10989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-02-11T16:15:19Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"283e597b2b9e229dce3020cf316674172fe583eba6d6bb3487758a407a11d9cb","abstract_canon_sha256":"1cc4c9cfc507158fb794156b4e42a017b29eef8d31181baeeb086b656cb11286"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:05.641136Z","signature_b64":"xVBlJPOFmFgD2Zrgnik2x9k6E5P/bZZvle3X8ORbzxpg1FExwh12YOaFF4muM2YsusvOkTYmWwbcHeLMwRWRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd5bf7156f0351d6c1e2f4e593ea458a5c509f4e491a94ef36d0eb11f44043d","last_reissued_at":"2026-05-20T00:03:05.640299Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:05.640299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational Optimality of F\\\"ollmer Processes in Generative Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Eric Vanden-Eijnden, Yifan Chen","submitted_at":"2026-02-11T16:15:19Z","abstract_excerpt":"We construct and analyze generative diffusions that transport a point mass to a prescribed target distribution over a finite time horizon using the stochastic interpolant framework. The drift is expressed as a conditional expectation that can be estimated from independent samples without simulating stochastic processes. We show that the diffusion coefficient can be tuned \\emph{a~posteriori} without changing the time-marginal distributions. Among all such tunings, we prove that minimizing the impact of estimation error on the path-space Kullback--Leibler divergence selects, in closed form, a F\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10989","kind":"arxiv","version":2},"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/2602.10989/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":"2602.10989","created_at":"2026-05-20T00:03:05.640458+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.10989v2","created_at":"2026-05-20T00:03:05.640458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.10989","created_at":"2026-05-20T00:03:05.640458+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7K364KW6A2R","created_at":"2026-05-20T00:03:05.640458+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7K364KW6A2R23A6","created_at":"2026-05-20T00:03:05.640458+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7K364KW","created_at":"2026-05-20T00:03:05.640458+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.18040","citing_title":"A note on connections between the F\\\"ollmer process and the denoising diffusion probabilistic model","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC","json":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC.json","graph_json":"https://pith.science/api/pith-number/L7K364KW6A2R23A6F5HFSPVELC/graph.json","events_json":"https://pith.science/api/pith-number/L7K364KW6A2R23A6F5HFSPVELC/events.json","paper":"https://pith.science/paper/L7K364KW"},"agent_actions":{"view_html":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC","download_json":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC.json","view_paper":"https://pith.science/paper/L7K364KW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.10989&json=true","fetch_graph":"https://pith.science/api/pith-number/L7K364KW6A2R23A6F5HFSPVELC/graph.json","fetch_events":"https://pith.science/api/pith-number/L7K364KW6A2R23A6F5HFSPVELC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC/action/storage_attestation","attest_author":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC/action/author_attestation","sign_citation":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC/action/citation_signature","submit_replication":"https://pith.science/pith/L7K364KW6A2R23A6F5HFSPVELC/action/replication_record"}},"created_at":"2026-05-20T00:03:05.640458+00:00","updated_at":"2026-05-20T00:03:05.640458+00:00"}