{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XX4OSIWSHYTK2J52SYHFSYF4IR","short_pith_number":"pith:XX4OSIWS","schema_version":"1.0","canonical_sha256":"bdf8e922d23e26ad27ba960e5960bc4474ceb94c383520d736709426b00c0c12","source":{"kind":"arxiv","id":"2505.02508","version":3},"attestation_state":"computed","paper":{"title":"Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Tan Minh Nguyen, Xin T. Tong, Yang Lyu, Yuchun Qian","submitted_at":"2025-05-05T09:40:41Z","abstract_excerpt":"Diffusion models are popular tools for generating new data samples, using a forward process that adds noise to data and a reverse process to denoise and produce samples. However, when the data distribution consists of n points, empirical diffusion models tend to reproduce existing data points, a phenomenon known as the memorization effect. Current literature often addresses this with complex machine learning techniques. This work shows that the memorization issue can be solved simply by applying an inertia update at the end of the empirical diffusion simulation. Our inertial diffusion model re"},"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":"2505.02508","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-05-05T09:40:41Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"8953fd4d3682753aa80c0231707b3354e43c667add598da63487000365bdf75f","abstract_canon_sha256":"a9387c112f438551227310ab1e5b64765f632ff20c240c759e9db26b66e5273c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:22.579432Z","signature_b64":"AMn3hmZTXX19X2o4X0ayxHpYlgKM0PtaYQxtg/GPTdpYTl83H9cJ2uA04B4onsU6EtT7IjwWqW7grVGwCDsqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdf8e922d23e26ad27ba960e5960bc4474ceb94c383520d736709426b00c0c12","last_reissued_at":"2026-07-05T11:47:22.578960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:22.578960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Tan Minh Nguyen, Xin T. Tong, Yang Lyu, Yuchun Qian","submitted_at":"2025-05-05T09:40:41Z","abstract_excerpt":"Diffusion models are popular tools for generating new data samples, using a forward process that adds noise to data and a reverse process to denoise and produce samples. However, when the data distribution consists of n points, empirical diffusion models tend to reproduce existing data points, a phenomenon known as the memorization effect. Current literature often addresses this with complex machine learning techniques. This work shows that the memorization issue can be solved simply by applying an inertia update at the end of the empirical diffusion simulation. Our inertial diffusion model re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02508","kind":"arxiv","version":3},"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/2505.02508/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":"2505.02508","created_at":"2026-07-05T11:47:22.579009+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.02508v3","created_at":"2026-07-05T11:47:22.579009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02508","created_at":"2026-07-05T11:47:22.579009+00:00"},{"alias_kind":"pith_short_12","alias_value":"XX4OSIWSHYTK","created_at":"2026-07-05T11:47:22.579009+00:00"},{"alias_kind":"pith_short_16","alias_value":"XX4OSIWSHYTK2J52","created_at":"2026-07-05T11:47:22.579009+00:00"},{"alias_kind":"pith_short_8","alias_value":"XX4OSIWS","created_at":"2026-07-05T11:47:22.579009+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.03820","citing_title":"A Quantitative Approximation Framework for Flow Distillation in Diffusion Models","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2605.15822","citing_title":"Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2512.16768","citing_title":"On The Hidden Biases of Flow Matching Samplers","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06077","citing_title":"Understanding diffusion models requires rethinking (again) generalization","ref_index":38,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR","json":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR.json","graph_json":"https://pith.science/api/pith-number/XX4OSIWSHYTK2J52SYHFSYF4IR/graph.json","events_json":"https://pith.science/api/pith-number/XX4OSIWSHYTK2J52SYHFSYF4IR/events.json","paper":"https://pith.science/paper/XX4OSIWS"},"agent_actions":{"view_html":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR","download_json":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR.json","view_paper":"https://pith.science/paper/XX4OSIWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.02508&json=true","fetch_graph":"https://pith.science/api/pith-number/XX4OSIWSHYTK2J52SYHFSYF4IR/graph.json","fetch_events":"https://pith.science/api/pith-number/XX4OSIWSHYTK2J52SYHFSYF4IR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR/action/storage_attestation","attest_author":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR/action/author_attestation","sign_citation":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR/action/citation_signature","submit_replication":"https://pith.science/pith/XX4OSIWSHYTK2J52SYHFSYF4IR/action/replication_record"}},"created_at":"2026-07-05T11:47:22.579009+00:00","updated_at":"2026-07-05T11:47:22.579009+00:00"}