{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BOK7LEZBD2UHUBSW25AD4VRHNE","short_pith_number":"pith:BOK7LEZB","schema_version":"1.0","canonical_sha256":"0b95f593211ea87a0656d7403e562769345b514f782e7b37cc7d42c1b17c5ed4","source":{"kind":"arxiv","id":"2606.06179","version":1},"attestation_state":"computed","paper":{"title":"Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Na\\\"il B. Khelifa, Ramji Venkataramanan, Richard E. Turner","submitted_at":"2026-06-04T13:53:38Z","abstract_excerpt":"Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behin"},"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":"2606.06179","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-04T13:53:38Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"716bdd083c1c728222ac7b2260c2a94f4ea289f80d9db111116b60be097b091b","abstract_canon_sha256":"4d3c24c0999c49ff0934148f06bf406e5df01887a8fa84b4aa9136ecde1edfef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:36.401824Z","signature_b64":"K9niAOUb7vIL+0I+4YQdPzA4vsiEbISdiS1/lykb6ST3rre0uoEDe+Z5bewQxEQM78Q9FA4U3NHTRoa5aPkeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b95f593211ea87a0656d7403e562769345b514f782e7b37cc7d42c1b17c5ed4","last_reissued_at":"2026-06-05T01:15:36.401205Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:36.401205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Na\\\"il B. Khelifa, Ramji Venkataramanan, Richard E. Turner","submitted_at":"2026-06-04T13:53:38Z","abstract_excerpt":"Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06179","kind":"arxiv","version":1},"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/2606.06179/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":"2606.06179","created_at":"2026-06-05T01:15:36.401302+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06179v1","created_at":"2026-06-05T01:15:36.401302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06179","created_at":"2026-06-05T01:15:36.401302+00:00"},{"alias_kind":"pith_short_12","alias_value":"BOK7LEZBD2UH","created_at":"2026-06-05T01:15:36.401302+00:00"},{"alias_kind":"pith_short_16","alias_value":"BOK7LEZBD2UHUBSW","created_at":"2026-06-05T01:15:36.401302+00:00"},{"alias_kind":"pith_short_8","alias_value":"BOK7LEZB","created_at":"2026-06-05T01:15:36.401302+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE","json":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE.json","graph_json":"https://pith.science/api/pith-number/BOK7LEZBD2UHUBSW25AD4VRHNE/graph.json","events_json":"https://pith.science/api/pith-number/BOK7LEZBD2UHUBSW25AD4VRHNE/events.json","paper":"https://pith.science/paper/BOK7LEZB"},"agent_actions":{"view_html":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE","download_json":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE.json","view_paper":"https://pith.science/paper/BOK7LEZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06179&json=true","fetch_graph":"https://pith.science/api/pith-number/BOK7LEZBD2UHUBSW25AD4VRHNE/graph.json","fetch_events":"https://pith.science/api/pith-number/BOK7LEZBD2UHUBSW25AD4VRHNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE/action/storage_attestation","attest_author":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE/action/author_attestation","sign_citation":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE/action/citation_signature","submit_replication":"https://pith.science/pith/BOK7LEZBD2UHUBSW25AD4VRHNE/action/replication_record"}},"created_at":"2026-06-05T01:15:36.401302+00:00","updated_at":"2026-06-05T01:15:36.401302+00:00"}