{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:A7CWVUURYQ3F4FCJFAKI5HXUBU","short_pith_number":"pith:A7CWVUUR","schema_version":"1.0","canonical_sha256":"07c56ad291c4365e144928148e9ef40d3f71731888b74e1fe8f02034d54075f0","source":{"kind":"arxiv","id":"2405.11326","version":1},"attestation_state":"computed","paper":{"title":"On the Trajectory Regularity of ODE-based Diffusion Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Can Wang, Chunhua Shen, Defang Chen, Siwei Lyu, Zhenyu Zhou","submitted_at":"2024-05-18T15:59:41Z","abstract_excerpt":"Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based "},"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":"2405.11326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-18T15:59:41Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"97f67c01b065691788de62b5d5f2b973b32699d77680acddb1e1452949aebf2c","abstract_canon_sha256":"f384edd7fafd8c89168b385138962dfaa8a91b49aac3d8e0638cf7987ec006be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:17.303345Z","signature_b64":"OxWUn14BP2+Q/l2HElmU/WwRVndi6K+bOVlJ/tN5kikAZFbmfYC3HzZH7IIXvoI7ON5zD2optyOzBUHujzDQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07c56ad291c4365e144928148e9ef40d3f71731888b74e1fe8f02034d54075f0","last_reissued_at":"2026-07-05T08:58:17.302819Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:17.302819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Trajectory Regularity of ODE-based Diffusion Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Can Wang, Chunhua Shen, Defang Chen, Siwei Lyu, Zhenyu Zhou","submitted_at":"2024-05-18T15:59:41Z","abstract_excerpt":"Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11326","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/2405.11326/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":"2405.11326","created_at":"2026-07-05T08:58:17.302880+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.11326v1","created_at":"2026-07-05T08:58:17.302880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11326","created_at":"2026-07-05T08:58:17.302880+00:00"},{"alias_kind":"pith_short_12","alias_value":"A7CWVUURYQ3F","created_at":"2026-07-05T08:58:17.302880+00:00"},{"alias_kind":"pith_short_16","alias_value":"A7CWVUURYQ3F4FCJ","created_at":"2026-07-05T08:58:17.302880+00:00"},{"alias_kind":"pith_short_8","alias_value":"A7CWVUUR","created_at":"2026-07-05T08:58:17.302880+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2602.07715","citing_title":"Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2512.13592","citing_title":"Image Diffusion Preview with Consistency Solver","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11547","citing_title":"Sharpen Your Flow: Sharpness-Aware Sampling for Flow Matching","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU","json":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU.json","graph_json":"https://pith.science/api/pith-number/A7CWVUURYQ3F4FCJFAKI5HXUBU/graph.json","events_json":"https://pith.science/api/pith-number/A7CWVUURYQ3F4FCJFAKI5HXUBU/events.json","paper":"https://pith.science/paper/A7CWVUUR"},"agent_actions":{"view_html":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU","download_json":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU.json","view_paper":"https://pith.science/paper/A7CWVUUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.11326&json=true","fetch_graph":"https://pith.science/api/pith-number/A7CWVUURYQ3F4FCJFAKI5HXUBU/graph.json","fetch_events":"https://pith.science/api/pith-number/A7CWVUURYQ3F4FCJFAKI5HXUBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU/action/storage_attestation","attest_author":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU/action/author_attestation","sign_citation":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU/action/citation_signature","submit_replication":"https://pith.science/pith/A7CWVUURYQ3F4FCJFAKI5HXUBU/action/replication_record"}},"created_at":"2026-07-05T08:58:17.302880+00:00","updated_at":"2026-07-05T08:58:17.302880+00:00"}