{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RLMUFPGX5PVLBIZQZBWKLHTSWO","short_pith_number":"pith:RLMUFPGX","schema_version":"1.0","canonical_sha256":"8ad942bcd7ebeab0a330c86ca59e72b398e08203f9046e884bc043d45a4c86e3","source":{"kind":"arxiv","id":"2409.18959","version":2},"attestation_state":"computed","paper":{"title":"O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions","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":"2024-09-27T17:59:10Z","abstract_excerpt":"Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their superior empirical performance, existing theoretical guarantees are often constrained by stringent assumptions or suboptimal convergence rates. In this paper, we establish a fast convergence theory for the denoising diffusion probabilistic model (DDPM), a widely used SDE-based sampler, under minimal assumptions. Our analysis shows that, provided $\\ell_{2}$-accu"},"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":"2409.18959","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-27T17:59:10Z","cross_cats_sorted":["cs.AI","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"073e7e2e84d30cc87e2a62e6ba97aa5b70fec3fe7b32d0ec89c9ee3ba5e8e441","abstract_canon_sha256":"e63260fbc4109f1fc278ac2b51c8ae984ef7792595478816d729da2340680f9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:03:46.555895Z","signature_b64":"P5EHGLFbYM53Cy0DRi12DIIKiWbBm52KueYrx7XXJ/A0g0Fu8lwjYjNKg4R8W119X4OA5T/r9WCMghuRmfc8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ad942bcd7ebeab0a330c86ca59e72b398e08203f9046e884bc043d45a4c86e3","last_reissued_at":"2026-07-05T10:03:46.555350Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:03:46.555350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions","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":"2024-09-27T17:59:10Z","abstract_excerpt":"Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their superior empirical performance, existing theoretical guarantees are often constrained by stringent assumptions or suboptimal convergence rates. In this paper, we establish a fast convergence theory for the denoising diffusion probabilistic model (DDPM), a widely used SDE-based sampler, under minimal assumptions. Our analysis shows that, provided $\\ell_{2}$-accu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.18959","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/2409.18959/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":"2409.18959","created_at":"2026-07-05T10:03:46.555420+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.18959v2","created_at":"2026-07-05T10:03:46.555420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.18959","created_at":"2026-07-05T10:03:46.555420+00:00"},{"alias_kind":"pith_short_12","alias_value":"RLMUFPGX5PVL","created_at":"2026-07-05T10:03:46.555420+00:00"},{"alias_kind":"pith_short_16","alias_value":"RLMUFPGX5PVLBIZQ","created_at":"2026-07-05T10:03:46.555420+00:00"},{"alias_kind":"pith_short_8","alias_value":"RLMUFPGX","created_at":"2026-07-05T10:03:46.555420+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.23627","citing_title":"Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2606.06624","citing_title":"Principles and Practice of Deep Representation Learning: or a Mathematical Theory of Memory","ref_index":55,"is_internal_anchor":false},{"citing_arxiv_id":"2507.12549","citing_title":"The Serial Scaling Hypothesis","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO","json":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO.json","graph_json":"https://pith.science/api/pith-number/RLMUFPGX5PVLBIZQZBWKLHTSWO/graph.json","events_json":"https://pith.science/api/pith-number/RLMUFPGX5PVLBIZQZBWKLHTSWO/events.json","paper":"https://pith.science/paper/RLMUFPGX"},"agent_actions":{"view_html":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO","download_json":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO.json","view_paper":"https://pith.science/paper/RLMUFPGX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.18959&json=true","fetch_graph":"https://pith.science/api/pith-number/RLMUFPGX5PVLBIZQZBWKLHTSWO/graph.json","fetch_events":"https://pith.science/api/pith-number/RLMUFPGX5PVLBIZQZBWKLHTSWO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO/action/storage_attestation","attest_author":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO/action/author_attestation","sign_citation":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO/action/citation_signature","submit_replication":"https://pith.science/pith/RLMUFPGX5PVLBIZQZBWKLHTSWO/action/replication_record"}},"created_at":"2026-07-05T10:03:46.555420+00:00","updated_at":"2026-07-05T10:03:46.555420+00:00"}