{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TXHVVOCUDOFQREUDCPOHTFWRAS","short_pith_number":"pith:TXHVVOCU","canonical_record":{"source":{"id":"2603.08155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-09T09:37:17Z","cross_cats_sorted":[],"title_canon_sha256":"6efece5cb074e39a42a6edd94354542e6460e38ab453d107793df4e80adedb62","abstract_canon_sha256":"c88afc9290c93646fcf4512cce8046c2580cbaa1aa723725ffee0df950158419"},"schema_version":"1.0"},"canonical_sha256":"9dcf5ab8541b8b08928313dc7996d10498dd03c81b6c09c9947022af60640317","source":{"kind":"arxiv","id":"2603.08155","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.08155","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2603.08155v3","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.08155","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"TXHVVOCUDOFQ","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"TXHVVOCUDOFQREUD","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"TXHVVOCU","created_at":"2026-05-21T01:04:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TXHVVOCUDOFQREUDCPOHTFWRAS","target":"record","payload":{"canonical_record":{"source":{"id":"2603.08155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-09T09:37:17Z","cross_cats_sorted":[],"title_canon_sha256":"6efece5cb074e39a42a6edd94354542e6460e38ab453d107793df4e80adedb62","abstract_canon_sha256":"c88afc9290c93646fcf4512cce8046c2580cbaa1aa723725ffee0df950158419"},"schema_version":"1.0"},"canonical_sha256":"9dcf5ab8541b8b08928313dc7996d10498dd03c81b6c09c9947022af60640317","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:24.422696Z","signature_b64":"NBZhYi4S4PmpR9PGUnquOZniBtc7OePEJnNI1112P0OnWzkur3bpDP007tMIRQXDwqR6jLwh6NakxBEpBQPMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dcf5ab8541b8b08928313dc7996d10498dd03c81b6c09c9947022af60640317","last_reissued_at":"2026-05-21T01:04:24.421698Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:24.421698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.08155","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRp7wn00xRRn3AuouVoe00AFc1s+WruN5npjgjAWNIOIpEnkIR7VjtuWoYU0bHqjtv9b/Ut/crU7FaXtZIvxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:45:55.780652Z"},"content_sha256":"37ef4a09ca5f9106c05f0e2d766f9cdd48421ac6e3945498d0af7f38cb11f37c","schema_version":"1.0","event_id":"sha256:37ef4a09ca5f9106c05f0e2d766f9cdd48421ac6e3945498d0af7f38cb11f37c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TXHVVOCUDOFQREUDCPOHTFWRAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bo Li, Fengxiang Yang, Hao Zhang, Jia Wang, Jiayang Gao, Jiayang Zou, Jinwei Chen, Luyao Fan, Peng-Tao Jiang, Shice Liu, Tianyi Zheng, Zheyu Zhang","submitted_at":"2026-03-09T09:37:17Z","abstract_excerpt":"Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a pri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that an exponential decay control function optimally aligns with the derived upper bounds on score discrepancy across timesteps and generalizes without task-specific fitting or post-hoc adjustments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"C²FG provides a time-dependent exponential decay control for classifier-free guidance based on theoretical upper bounds on conditional-unconditional score discrepancies in diffusion processes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"14723b9c1ef802dab28b74bc6ab913d342cc749d920eb36704224e2303308fc9"},"source":{"id":"2603.08155","kind":"arxiv","version":3},"verdict":{"id":"beefc209-7120-4278-b23e-045e98197c4b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T14:57:41.766970Z","strongest_claim":"we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance.","one_line_summary":"C²FG provides a time-dependent exponential decay control for classifier-free guidance based on theoretical upper bounds on conditional-unconditional score discrepancies in diffusion processes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that an exponential decay control function optimally aligns with the derived upper bounds on score discrepancy across timesteps and generalizes without task-specific fitting or post-hoc adjustments.","pith_extraction_headline":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.08155/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":2,"snapshot_sha256":"5c81e712aacd489510c8be41a86766bd094a70d45cf635b8fec02c7de892bbaf"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"beefc209-7120-4278-b23e-045e98197c4b"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RtWA5kgNIxV7VA5clcCFvb8BHnUo8oJsj3r31P1TbX1HMoBRR+bBPSCvy/d0ChG+0/57MyJAB7KpQFzyNeWeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:45:55.781138Z"},"content_sha256":"a207703b2057662fe34859ac70a5065a1a102158511d4f6319a813bbd0694f2c","schema_version":"1.0","event_id":"sha256:a207703b2057662fe34859ac70a5065a1a102158511d4f6319a813bbd0694f2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/bundle.json","state_url":"https://pith.science/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/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":"2026-06-03T22:45:55Z","links":{"resolver":"https://pith.science/pith/TXHVVOCUDOFQREUDCPOHTFWRAS","bundle":"https://pith.science/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/bundle.json","state":"https://pith.science/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXHVVOCUDOFQREUDCPOHTFWRAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TXHVVOCUDOFQREUDCPOHTFWRAS","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":"c88afc9290c93646fcf4512cce8046c2580cbaa1aa723725ffee0df950158419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-09T09:37:17Z","title_canon_sha256":"6efece5cb074e39a42a6edd94354542e6460e38ab453d107793df4e80adedb62"},"schema_version":"1.0","source":{"id":"2603.08155","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.08155","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2603.08155v3","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.08155","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"TXHVVOCUDOFQ","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"TXHVVOCUDOFQREUD","created_at":"2026-05-21T01:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"TXHVVOCU","created_at":"2026-05-21T01:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:a207703b2057662fe34859ac70a5065a1a102158511d4f6319a813bbd0694f2c","target":"graph","created_at":"2026-05-21T01:04:24Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that an exponential decay control function optimally aligns with the derived upper bounds on score discrepancy across timesteps and generalizes without task-specific fitting or post-hoc adjustments."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"C²FG provides a time-dependent exponential decay control for classifier-free guidance based on theoretical upper bounds on conditional-unconditional score discrepancies in diffusion processes."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models."}],"snapshot_sha256":"14723b9c1ef802dab28b74bc6ab913d342cc749d920eb36704224e2303308fc9"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5c81e712aacd489510c8be41a86766bd094a70d45cf635b8fec02c7de892bbaf"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.08155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a pri","authors_text":"Bo Li, Fengxiang Yang, Hao Zhang, Jia Wang, Jiayang Gao, Jiayang Zou, Jinwei Chen, Luyao Fan, Peng-Tao Jiang, Shice Liu, Tianyi Zheng, Zheyu Zhang","cross_cats":[],"headline":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-09T09:37:17Z","title":"C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.08155","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-15T14:57:41.766970Z","id":"beefc209-7120-4278-b23e-045e98197c4b","model_set":{"reader":"grok-4.3"},"one_line_summary":"C²FG provides a time-dependent exponential decay control for classifier-free guidance based on theoretical upper bounds on conditional-unconditional score discrepancies in diffusion processes.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Upper bounds on score discrepancy between conditional and unconditional distributions justify replacing fixed guidance weights with time-dependent control in diffusion models.","strongest_claim":"we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance.","weakest_assumption":"The assumption that an exponential decay control function optimally aligns with the derived upper bounds on score discrepancy across timesteps and generalizes without task-specific fitting or post-hoc adjustments."}},"verdict_id":"beefc209-7120-4278-b23e-045e98197c4b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:37ef4a09ca5f9106c05f0e2d766f9cdd48421ac6e3945498d0af7f38cb11f37c","target":"record","created_at":"2026-05-21T01:04:24Z","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":"c88afc9290c93646fcf4512cce8046c2580cbaa1aa723725ffee0df950158419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-03-09T09:37:17Z","title_canon_sha256":"6efece5cb074e39a42a6edd94354542e6460e38ab453d107793df4e80adedb62"},"schema_version":"1.0","source":{"id":"2603.08155","kind":"arxiv","version":3}},"canonical_sha256":"9dcf5ab8541b8b08928313dc7996d10498dd03c81b6c09c9947022af60640317","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dcf5ab8541b8b08928313dc7996d10498dd03c81b6c09c9947022af60640317","first_computed_at":"2026-05-21T01:04:24.421698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:24.421698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NBZhYi4S4PmpR9PGUnquOZniBtc7OePEJnNI1112P0OnWzkur3bpDP007tMIRQXDwqR6jLwh6NakxBEpBQPMAg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:24.422696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.08155","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37ef4a09ca5f9106c05f0e2d766f9cdd48421ac6e3945498d0af7f38cb11f37c","sha256:a207703b2057662fe34859ac70a5065a1a102158511d4f6319a813bbd0694f2c"],"state_sha256":"045a3b927dd91644d6a4b17538a43728e8ad9f67257ed51630a70f69f8b89efa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8WfcAO8Fh1IBC0zqeZBrC1luyDfRNlFM4BEF7AOnvydkkybIIPSXND7hdJTK9o/N1m08/ZS6dTUCJSafb6DCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:45:55.783428Z","bundle_sha256":"c381584e7f41a8ef7791a5eef6e2b3d72143eedaac0696b3e59a1869b965aa3b"}}