{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YYOAGYFH64S6YV7XOKI22JCYDB","short_pith_number":"pith:YYOAGYFH","canonical_record":{"source":{"id":"2302.07194","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-14T17:02:35Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1c78b4d8427b726c1c12f138b781b89d57e144eb6e5bf595860f8a49e0ec0901","abstract_canon_sha256":"df7c2e0bce83be76b64c4fe9c11ac9b0980ed11bfc6020b4d6063a74a8e54f8b"},"schema_version":"1.0"},"canonical_sha256":"c61c0360a7f725ec57f77291ad2458186d73e0c6043dd30c27b7ea01e92abad1","source":{"kind":"arxiv","id":"2302.07194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.07194","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"2302.07194v1","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.07194","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"YYOAGYFH64S6","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_16","alias_value":"YYOAGYFH64S6YV7X","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_8","alias_value":"YYOAGYFH","created_at":"2026-07-05T05:41:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YYOAGYFH64S6YV7XOKI22JCYDB","target":"record","payload":{"canonical_record":{"source":{"id":"2302.07194","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-14T17:02:35Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1c78b4d8427b726c1c12f138b781b89d57e144eb6e5bf595860f8a49e0ec0901","abstract_canon_sha256":"df7c2e0bce83be76b64c4fe9c11ac9b0980ed11bfc6020b4d6063a74a8e54f8b"},"schema_version":"1.0"},"canonical_sha256":"c61c0360a7f725ec57f77291ad2458186d73e0c6043dd30c27b7ea01e92abad1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:41:48.127256Z","signature_b64":"hHArgQUTPUYQ2Fz5IzkhbAv8fSBWz7vjTBDYvCnKbez4szlLIFwtsOjoudDMD9ywibR0jBIVR0QR9W2Hf6dWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c61c0360a7f725ec57f77291ad2458186d73e0c6043dd30c27b7ea01e92abad1","last_reissued_at":"2026-07-05T05:41:48.126785Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:41:48.126785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.07194","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":"2026-07-05T05:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEc9ctbcimwZJ6ZJBkCWjmFdKzW4P6+s/HTDASCraoc70Suqh6TWkgiZjdGqifQTyRHLXwXusK7vF6IlZZ/6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T00:01:08.825598Z"},"content_sha256":"24c58edf4b801c9e1a0f460ecaa2d690f4d1f7196ffe92beb8ee9edbbf3f9d9c","schema_version":"1.0","event_id":"sha256:24c58edf4b801c9e1a0f460ecaa2d690f4d1f7196ffe92beb8ee9edbbf3f9d9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YYOAGYFH64S6YV7XOKI22JCYDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Kaixuan Huang, Mengdi Wang, Minshuo Chen, Tuo Zhao","submitted_at":"2023-02-14T17:02:35Z","abstract_excerpt":"Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07194","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/2302.07194/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":"2026-07-05T05:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBkK/7+TSk8RP3rIXjK53S6cErjXeKBizzcxBXTXpkvf5Zghg/zu/0eqAuCtD3p//rkZ0edQZNvIyy2mBUSZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-16T00:01:08.825974Z"},"content_sha256":"5ad79539a06ceb46bf7dee81ab521e6ae13ceb0ff3376422389257af64a4d61c","schema_version":"1.0","event_id":"sha256:5ad79539a06ceb46bf7dee81ab521e6ae13ceb0ff3376422389257af64a4d61c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYOAGYFH64S6YV7XOKI22JCYDB/bundle.json","state_url":"https://pith.science/pith/YYOAGYFH64S6YV7XOKI22JCYDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYOAGYFH64S6YV7XOKI22JCYDB/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":"2026-07-16T00:01:08Z","links":{"resolver":"https://pith.science/pith/YYOAGYFH64S6YV7XOKI22JCYDB","bundle":"https://pith.science/pith/YYOAGYFH64S6YV7XOKI22JCYDB/bundle.json","state":"https://pith.science/pith/YYOAGYFH64S6YV7XOKI22JCYDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYOAGYFH64S6YV7XOKI22JCYDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YYOAGYFH64S6YV7XOKI22JCYDB","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":"df7c2e0bce83be76b64c4fe9c11ac9b0980ed11bfc6020b4d6063a74a8e54f8b","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-14T17:02:35Z","title_canon_sha256":"1c78b4d8427b726c1c12f138b781b89d57e144eb6e5bf595860f8a49e0ec0901"},"schema_version":"1.0","source":{"id":"2302.07194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.07194","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"2302.07194v1","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.07194","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"YYOAGYFH64S6","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_16","alias_value":"YYOAGYFH64S6YV7X","created_at":"2026-07-05T05:41:48Z"},{"alias_kind":"pith_short_8","alias_value":"YYOAGYFH","created_at":"2026-07-05T05:41:48Z"}],"graph_snapshots":[{"event_id":"sha256:5ad79539a06ceb46bf7dee81ab521e6ae13ceb0ff3376422389257af64a4d61c","target":"graph","created_at":"2026-07-05T05:41:48Z","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/2302.07194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based o","authors_text":"Kaixuan Huang, Mengdi Wang, Minshuo Chen, Tuo Zhao","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-14T17:02:35Z","title":"Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07194","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":"sha256:24c58edf4b801c9e1a0f460ecaa2d690f4d1f7196ffe92beb8ee9edbbf3f9d9c","target":"record","created_at":"2026-07-05T05:41:48Z","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":"df7c2e0bce83be76b64c4fe9c11ac9b0980ed11bfc6020b4d6063a74a8e54f8b","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2023-02-14T17:02:35Z","title_canon_sha256":"1c78b4d8427b726c1c12f138b781b89d57e144eb6e5bf595860f8a49e0ec0901"},"schema_version":"1.0","source":{"id":"2302.07194","kind":"arxiv","version":1}},"canonical_sha256":"c61c0360a7f725ec57f77291ad2458186d73e0c6043dd30c27b7ea01e92abad1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c61c0360a7f725ec57f77291ad2458186d73e0c6043dd30c27b7ea01e92abad1","first_computed_at":"2026-07-05T05:41:48.126785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:41:48.126785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHArgQUTPUYQ2Fz5IzkhbAv8fSBWz7vjTBDYvCnKbez4szlLIFwtsOjoudDMD9ywibR0jBIVR0QR9W2Hf6dWDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:41:48.127256Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.07194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24c58edf4b801c9e1a0f460ecaa2d690f4d1f7196ffe92beb8ee9edbbf3f9d9c","sha256:5ad79539a06ceb46bf7dee81ab521e6ae13ceb0ff3376422389257af64a4d61c"],"state_sha256":"40b1f4679206486fe94c3f9c6a403433c8c91e125e19b2aee05a72b34824aefe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hy/ZzLDjJeVQ2c3iQwbtbmidKupYgl6rqcCK6LLs2JxEy/XtuuWL0QgJk3VIrqu9dyO4kMBJdz3ryTFPHowyCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-16T00:01:08.828515Z","bundle_sha256":"066c540e4417d2aab04bf3ebad5a54af493ae76c8e11d2229b4797144c4a1a78"}}