{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:R6RNXLY66FAERIG6XTZPIUYCHJ","short_pith_number":"pith:R6RNXLY6","canonical_record":{"source":{"id":"2303.01861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-03T11:31:55Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2a5c55cea4d06320be47b439e0a1feb2b5344d6532217c1f2a6ba2ddb8a92be8","abstract_canon_sha256":"1bca3218296371d093cd6df3da3c1e93ecc9d37f01d5b95f9c081b042d4d49a3"},"schema_version":"1.0"},"canonical_sha256":"8fa2dbaf1ef14048a0debcf2f453023a60d0a07d2a1305afe9d2c251f12b0848","source":{"kind":"arxiv","id":"2303.01861","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01861","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01861v1","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01861","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"R6RNXLY66FAE","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_16","alias_value":"R6RNXLY66FAERIG6","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_8","alias_value":"R6RNXLY6","created_at":"2026-07-05T05:47:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:R6RNXLY66FAERIG6XTZPIUYCHJ","target":"record","payload":{"canonical_record":{"source":{"id":"2303.01861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-03T11:31:55Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2a5c55cea4d06320be47b439e0a1feb2b5344d6532217c1f2a6ba2ddb8a92be8","abstract_canon_sha256":"1bca3218296371d093cd6df3da3c1e93ecc9d37f01d5b95f9c081b042d4d49a3"},"schema_version":"1.0"},"canonical_sha256":"8fa2dbaf1ef14048a0debcf2f453023a60d0a07d2a1305afe9d2c251f12b0848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:50.092801Z","signature_b64":"JPeJ9OKbfosVCKYygOIP2qLfvpfsIGAfplv2eNPvNsu6EDL5w3xD1rBqPlA9DfXX6S5vuQtbgf8RTy5rMJTUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fa2dbaf1ef14048a0debcf2f453023a60d0a07d2a1305afe9d2c251f12b0848","last_reissued_at":"2026-07-05T05:47:50.092247Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:50.092247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.01861","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HFlzd871ZLV0DRaBdIqj9H2S4ZRjFA71AZtYZrmXB0qJV6yEBQXBHRKXi/RB4SgzLzli9sWSyct3W1an49yzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:32:41.106909Z"},"content_sha256":"14472797dbfc385b447afd4b0a10a068a9305baa1b8ea928aa9b0c515c2afe5d","schema_version":"1.0","event_id":"sha256:14472797dbfc385b447afd4b0a10a068a9305baa1b8ea928aa9b0c515c2afe5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:R6RNXLY66FAERIG6XTZPIUYCHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion Models are Minimax Optimal Distribution Estimators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Kazusato Oko, Shunta Akiyama, Taiji Suzuki","submitted_at":"2023-03-03T11:31:55Z","abstract_excerpt":"While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01861","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/2303.01861/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlgJoVAt8WztRRBzjQ23gOqq6232ZRnoLIx6cKKhhn7gpSr24a9p06tMRV7iURGzKWowucQ1WrS1FjRBj0VNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:32:41.107398Z"},"content_sha256":"07b70db3ad3d01f4c6e1919293db31e742c1e25059b714bf6c01f91ead01e90d","schema_version":"1.0","event_id":"sha256:07b70db3ad3d01f4c6e1919293db31e742c1e25059b714bf6c01f91ead01e90d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/bundle.json","state_url":"https://pith.science/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T09:32:41Z","links":{"resolver":"https://pith.science/pith/R6RNXLY66FAERIG6XTZPIUYCHJ","bundle":"https://pith.science/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/bundle.json","state":"https://pith.science/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6RNXLY66FAERIG6XTZPIUYCHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:R6RNXLY66FAERIG6XTZPIUYCHJ","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":"1bca3218296371d093cd6df3da3c1e93ecc9d37f01d5b95f9c081b042d4d49a3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-03T11:31:55Z","title_canon_sha256":"2a5c55cea4d06320be47b439e0a1feb2b5344d6532217c1f2a6ba2ddb8a92be8"},"schema_version":"1.0","source":{"id":"2303.01861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01861","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01861v1","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01861","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"R6RNXLY66FAE","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_16","alias_value":"R6RNXLY66FAERIG6","created_at":"2026-07-05T05:47:50Z"},{"alias_kind":"pith_short_8","alias_value":"R6RNXLY6","created_at":"2026-07-05T05:47:50Z"}],"graph_snapshots":[{"event_id":"sha256:07b70db3ad3d01f4c6e1919293db31e742c1e25059b714bf6c01f91ead01e90d","target":"graph","created_at":"2026-07-05T05:47:50Z","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/2303.01861/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstei","authors_text":"Kazusato Oko, Shunta Akiyama, Taiji Suzuki","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-03T11:31:55Z","title":"Diffusion Models are Minimax Optimal Distribution Estimators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01861","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":"sha256:14472797dbfc385b447afd4b0a10a068a9305baa1b8ea928aa9b0c515c2afe5d","target":"record","created_at":"2026-07-05T05:47:50Z","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":"1bca3218296371d093cd6df3da3c1e93ecc9d37f01d5b95f9c081b042d4d49a3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-03T11:31:55Z","title_canon_sha256":"2a5c55cea4d06320be47b439e0a1feb2b5344d6532217c1f2a6ba2ddb8a92be8"},"schema_version":"1.0","source":{"id":"2303.01861","kind":"arxiv","version":1}},"canonical_sha256":"8fa2dbaf1ef14048a0debcf2f453023a60d0a07d2a1305afe9d2c251f12b0848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fa2dbaf1ef14048a0debcf2f453023a60d0a07d2a1305afe9d2c251f12b0848","first_computed_at":"2026-07-05T05:47:50.092247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:50.092247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JPeJ9OKbfosVCKYygOIP2qLfvpfsIGAfplv2eNPvNsu6EDL5w3xD1rBqPlA9DfXX6S5vuQtbgf8RTy5rMJTUDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:50.092801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.01861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14472797dbfc385b447afd4b0a10a068a9305baa1b8ea928aa9b0c515c2afe5d","sha256:07b70db3ad3d01f4c6e1919293db31e742c1e25059b714bf6c01f91ead01e90d"],"state_sha256":"48012a4e62c54b85dae37e8161acc02f169d32dcd58495ebac7d4639ebcd837a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXS4wf0FkWarYxpsFaeTUooAV4Nn6Dtvjb5nvXVhiASIXIH9g+RsrFcx+pDNRatWFS1WNS/Fkiy+AEc2ttOvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:32:41.112287Z","bundle_sha256":"5cfc22e37bccd1a3f2eed76e712d91960513032cfee6360c1d6ea5b35f5ad165"}}