{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WAUPDHGBM26GEEPNBUDCMLZXWX","short_pith_number":"pith:WAUPDHGB","canonical_record":{"source":{"id":"2405.14861","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T17:59:10Z","cross_cats_sorted":["cs.AI","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"de4c7413df71dc36cc4bc9350dd2c4c24a74cd62b2c748f78a4c2ea432cf2c96","abstract_canon_sha256":"7c49d6c23568953f898335f9776f6f1b48b557870fbd1429431734a0ad59a8c8"},"schema_version":"1.0"},"canonical_sha256":"b028f19cc166bc6211ed0d06262f37b5d13b917fcac25ec2d122a97f7b636391","source":{"kind":"arxiv","id":"2405.14861","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14861","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14861v2","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14861","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"WAUPDHGBM26G","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_16","alias_value":"WAUPDHGBM26GEEPN","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_8","alias_value":"WAUPDHGB","created_at":"2026-07-05T09:55:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WAUPDHGBM26GEEPNBUDCMLZXWX","target":"record","payload":{"canonical_record":{"source":{"id":"2405.14861","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T17:59:10Z","cross_cats_sorted":["cs.AI","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"de4c7413df71dc36cc4bc9350dd2c4c24a74cd62b2c748f78a4c2ea432cf2c96","abstract_canon_sha256":"7c49d6c23568953f898335f9776f6f1b48b557870fbd1429431734a0ad59a8c8"},"schema_version":"1.0"},"canonical_sha256":"b028f19cc166bc6211ed0d06262f37b5d13b917fcac25ec2d122a97f7b636391","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:33.328426Z","signature_b64":"NLPN6qoUAATZbB0Po9UftsdauH9W+yJJhojFPJp6sfk715aErnna3p5i83Pw3mhIJOQKHHQLW1nsW+5q1eMbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b028f19cc166bc6211ed0d06262f37b5d13b917fcac25ec2d122a97f7b636391","last_reissued_at":"2026-07-05T09:55:33.327944Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:33.327944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.14861","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TGGK+8OtwYJSy58NPRlEMmpd61dlrJy+HVaFq/N/yoDvEtYXGaTkFSY76J8TCys0o0sF6JENjeXaFtCMUD0uBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:40:30.831697Z"},"content_sha256":"f52750b2a473e04b35afdf24ef7465e01778ae013aeb2276f1946a3ad3263c6f","schema_version":"1.0","event_id":"sha256:f52750b2a473e04b35afdf24ef7465e01778ae013aeb2276f1946a3ad3263c6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WAUPDHGBM26GEEPNBUDCMLZXWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Gen Li, Yuling Yan","submitted_at":"2024-05-23T17:59:10Z","abstract_excerpt":"This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of natural image distributions. Despite previous efforts to understand the data generation process of diffusion models, existing theoretical support remains highly suboptimal in the presence of low-dimensional structure, which we strengthen in this paper. For the popular Denoising Diffusion Probabilistic Model (DDPM), we find that the dependency of the error in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14861","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/2405.14861/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":"2026-07-05T09:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/06pm4a4riLQTvYD6WQ9F2JePDhaW7OtWayr+/MUf5b4N7PS+wF3Pz9QiXzztM9D+1uTrXdsRAtZb3uLi9u/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:40:30.832328Z"},"content_sha256":"7194a75e37f89f1cb7e237d540b06577e74b32817435a61c5b707b7a31202a21","schema_version":"1.0","event_id":"sha256:7194a75e37f89f1cb7e237d540b06577e74b32817435a61c5b707b7a31202a21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/bundle.json","state_url":"https://pith.science/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/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":"2026-08-08T14:40:30Z","links":{"resolver":"https://pith.science/pith/WAUPDHGBM26GEEPNBUDCMLZXWX","bundle":"https://pith.science/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/bundle.json","state":"https://pith.science/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAUPDHGBM26GEEPNBUDCMLZXWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WAUPDHGBM26GEEPNBUDCMLZXWX","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":"7c49d6c23568953f898335f9776f6f1b48b557870fbd1429431734a0ad59a8c8","cross_cats_sorted":["cs.AI","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T17:59:10Z","title_canon_sha256":"de4c7413df71dc36cc4bc9350dd2c4c24a74cd62b2c748f78a4c2ea432cf2c96"},"schema_version":"1.0","source":{"id":"2405.14861","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14861","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14861v2","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14861","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"WAUPDHGBM26G","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_16","alias_value":"WAUPDHGBM26GEEPN","created_at":"2026-07-05T09:55:33Z"},{"alias_kind":"pith_short_8","alias_value":"WAUPDHGB","created_at":"2026-07-05T09:55:33Z"}],"graph_snapshots":[{"event_id":"sha256:7194a75e37f89f1cb7e237d540b06577e74b32817435a61c5b707b7a31202a21","target":"graph","created_at":"2026-07-05T09:55:33Z","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/2405.14861/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of natural image distributions. Despite previous efforts to understand the data generation process of diffusion models, existing theoretical support remains highly suboptimal in the presence of low-dimensional structure, which we strengthen in this paper. For the popular Denoising Diffusion Probabilistic Model (DDPM), we find that the dependency of the error in","authors_text":"Gen Li, Yuling Yan","cross_cats":["cs.AI","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T17:59:10Z","title":"Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14861","kind":"arxiv","version":2},"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:f52750b2a473e04b35afdf24ef7465e01778ae013aeb2276f1946a3ad3263c6f","target":"record","created_at":"2026-07-05T09:55:33Z","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":"7c49d6c23568953f898335f9776f6f1b48b557870fbd1429431734a0ad59a8c8","cross_cats_sorted":["cs.AI","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-23T17:59:10Z","title_canon_sha256":"de4c7413df71dc36cc4bc9350dd2c4c24a74cd62b2c748f78a4c2ea432cf2c96"},"schema_version":"1.0","source":{"id":"2405.14861","kind":"arxiv","version":2}},"canonical_sha256":"b028f19cc166bc6211ed0d06262f37b5d13b917fcac25ec2d122a97f7b636391","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b028f19cc166bc6211ed0d06262f37b5d13b917fcac25ec2d122a97f7b636391","first_computed_at":"2026-07-05T09:55:33.327944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:33.327944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NLPN6qoUAATZbB0Po9UftsdauH9W+yJJhojFPJp6sfk715aErnna3p5i83Pw3mhIJOQKHHQLW1nsW+5q1eMbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:33.328426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.14861","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f52750b2a473e04b35afdf24ef7465e01778ae013aeb2276f1946a3ad3263c6f","sha256:7194a75e37f89f1cb7e237d540b06577e74b32817435a61c5b707b7a31202a21"],"state_sha256":"304b7e40624972c1028bdc6a85b3e73cacf4ea28a86db76f8f310a3e3aade0f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CBEwQsKAUdc1KXoAyATzJ5p91Fb2l5jCsI5IgUetWQ7ouWJHpfAvSntJS6Psqy3Azmb0aSBGgohrjzWc0hQJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:40:30.837896Z","bundle_sha256":"db5d68f1699905bf4596db8073b047ee1684ea920f232732eed8b5da0adc6384"}}