{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BOK7LEZBD2UHUBSW25AD4VRHNE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4d3c24c0999c49ff0934148f06bf406e5df01887a8fa84b4aa9136ecde1edfef","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-04T13:53:38Z","title_canon_sha256":"716bdd083c1c728222ac7b2260c2a94f4ea289f80d9db111116b60be097b091b"},"schema_version":"1.0","source":{"id":"2606.06179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06179","created_at":"2026-06-05T01:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06179v1","created_at":"2026-06-05T01:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06179","created_at":"2026-06-05T01:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"BOK7LEZBD2UH","created_at":"2026-06-05T01:15:36Z"},{"alias_kind":"pith_short_16","alias_value":"BOK7LEZBD2UHUBSW","created_at":"2026-06-05T01:15:36Z"},{"alias_kind":"pith_short_8","alias_value":"BOK7LEZB","created_at":"2026-06-05T01:15:36Z"}],"graph_snapshots":[{"event_id":"sha256:67dc9ebc05d8448ff375afd52d72398608899bd43053bd6db6364a672bebbd16","target":"graph","created_at":"2026-06-05T01:15:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06179/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Na\\\"il B. Khelifa, Ramji Venkataramanan, Richard E. Turner","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-04T13:53:38Z","title":"Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06179","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:814d4a40b4b9534fea698a43f787edb1ee602af204ae32923de17a6a0dabe112","target":"record","created_at":"2026-06-05T01:15:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4d3c24c0999c49ff0934148f06bf406e5df01887a8fa84b4aa9136ecde1edfef","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-04T13:53:38Z","title_canon_sha256":"716bdd083c1c728222ac7b2260c2a94f4ea289f80d9db111116b60be097b091b"},"schema_version":"1.0","source":{"id":"2606.06179","kind":"arxiv","version":1}},"canonical_sha256":"0b95f593211ea87a0656d7403e562769345b514f782e7b37cc7d42c1b17c5ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b95f593211ea87a0656d7403e562769345b514f782e7b37cc7d42c1b17c5ed4","first_computed_at":"2026-06-05T01:15:36.401205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:36.401205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K9niAOUb7vIL+0I+4YQdPzA4vsiEbISdiS1/lykb6ST3rre0uoEDe+Z5bewQxEQM78Q9FA4U3NHTRoa5aPkeDA==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:36.401824Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:814d4a40b4b9534fea698a43f787edb1ee602af204ae32923de17a6a0dabe112","sha256:67dc9ebc05d8448ff375afd52d72398608899bd43053bd6db6364a672bebbd16"],"state_sha256":"6349dfde1200d2b260aae698ac4e6546408c9de92123b6ab2fcea14036aff329"}