{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:W4T6BLLZGSA75R2JLUPQSJXIAY","short_pith_number":"pith:W4T6BLLZ","canonical_record":{"source":{"id":"2402.02149","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-02-03T13:35:39Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"940307ffb8ed180d6c2a1605db07c229409fae261b9f57c9914a222f61dc5d73","abstract_canon_sha256":"89acd01740c20537b1a9e4d0f9469c37e01502aec447a171c30b8943839577a1"},"schema_version":"1.0"},"canonical_sha256":"b727e0ad793481fec7495d1f0926e8061a0ee7cb40aab2f9e6e5bdb1763a445a","source":{"kind":"arxiv","id":"2402.02149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02149","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02149v2","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02149","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"W4T6BLLZGSA7","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"W4T6BLLZGSA75R2J","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"W4T6BLLZ","created_at":"2026-07-05T08:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:W4T6BLLZGSA75R2JLUPQSJXIAY","target":"record","payload":{"canonical_record":{"source":{"id":"2402.02149","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-02-03T13:35:39Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"940307ffb8ed180d6c2a1605db07c229409fae261b9f57c9914a222f61dc5d73","abstract_canon_sha256":"89acd01740c20537b1a9e4d0f9469c37e01502aec447a171c30b8943839577a1"},"schema_version":"1.0"},"canonical_sha256":"b727e0ad793481fec7495d1f0926e8061a0ee7cb40aab2f9e6e5bdb1763a445a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:18.643953Z","signature_b64":"wgdi/4o7mEY1jYKD4G7uFS8Wkh7eXxVO+AH1zL3KqeslPTmrFBb9F00SFLypVlCDxvagIRkO0ugbLxdaOkSFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b727e0ad793481fec7495d1f0926e8061a0ee7cb40aab2f9e6e5bdb1763a445a","last_reissued_at":"2026-07-05T08:26:18.643400Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:18.643400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.02149","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":"2026-07-05T08:26:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VAQBDhGmi0ycXbgTsFttxNESu85NVuccVvuSHWJG3LOTwyAz7FRQwJPhinZV8gK72y7PkWEoMo9QhULc4pKoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:28:34.070614Z"},"content_sha256":"bd2f057d09272a5877752aeb68e4bea7f8d98e6aad48a86159b519c3d2375c38","schema_version":"1.0","event_id":"sha256:bd2f057d09272a5877752aeb68e4bea7f8d98e6aad48a86159b519c3d2375c38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:W4T6BLLZGSA75R2JLUPQSJXIAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Chenglin Li, Hongkai Xiong, Junni Zou, Nuoqian Xiao, Wenrui Dai, Xinyu Peng, Ziyang Zheng","submitted_at":"2024-02-03T13:35:39Z","abstract_excerpt":"Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02149","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/2402.02149/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":"2026-07-05T08:26:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWP/MhioeYCHUT38jzBOQIjy78womxkhUhW9oUt+MmE9QSrgvX3Avgu3y+e2ZGIXTxRdfxS1bDzCaWl7CKG3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:28:34.071433Z"},"content_sha256":"5104c63416121cb50211801917f297afe63acb23eec6021de03b209537454727","schema_version":"1.0","event_id":"sha256:5104c63416121cb50211801917f297afe63acb23eec6021de03b209537454727"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/bundle.json","state_url":"https://pith.science/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/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":"2026-08-09T06:28:34Z","links":{"resolver":"https://pith.science/pith/W4T6BLLZGSA75R2JLUPQSJXIAY","bundle":"https://pith.science/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/bundle.json","state":"https://pith.science/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W4T6BLLZGSA75R2JLUPQSJXIAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W4T6BLLZGSA75R2JLUPQSJXIAY","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":"89acd01740c20537b1a9e4d0f9469c37e01502aec447a171c30b8943839577a1","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-02-03T13:35:39Z","title_canon_sha256":"940307ffb8ed180d6c2a1605db07c229409fae261b9f57c9914a222f61dc5d73"},"schema_version":"1.0","source":{"id":"2402.02149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02149","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02149v2","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02149","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"W4T6BLLZGSA7","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"W4T6BLLZGSA75R2J","created_at":"2026-07-05T08:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"W4T6BLLZ","created_at":"2026-07-05T08:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:5104c63416121cb50211801917f297afe63acb23eec6021de03b209537454727","target":"graph","created_at":"2026-07-05T08:26:18Z","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/2402.02149/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a Gaussian approximation with hand-crafted isotropic covariance for the intractable denoising posterior to approximate the conditional posterior mean. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation. To achieve posterior covariance optimization without retraining, we prov","authors_text":"Chenglin Li, Hongkai Xiong, Junni Zou, Nuoqian Xiao, Wenrui Dai, Xinyu Peng, Ziyang Zheng","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-02-03T13:35:39Z","title":"Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02149","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:bd2f057d09272a5877752aeb68e4bea7f8d98e6aad48a86159b519c3d2375c38","target":"record","created_at":"2026-07-05T08:26:18Z","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":"89acd01740c20537b1a9e4d0f9469c37e01502aec447a171c30b8943839577a1","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CV","submitted_at":"2024-02-03T13:35:39Z","title_canon_sha256":"940307ffb8ed180d6c2a1605db07c229409fae261b9f57c9914a222f61dc5d73"},"schema_version":"1.0","source":{"id":"2402.02149","kind":"arxiv","version":2}},"canonical_sha256":"b727e0ad793481fec7495d1f0926e8061a0ee7cb40aab2f9e6e5bdb1763a445a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b727e0ad793481fec7495d1f0926e8061a0ee7cb40aab2f9e6e5bdb1763a445a","first_computed_at":"2026-07-05T08:26:18.643400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:18.643400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgdi/4o7mEY1jYKD4G7uFS8Wkh7eXxVO+AH1zL3KqeslPTmrFBb9F00SFLypVlCDxvagIRkO0ugbLxdaOkSFAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:18.643953Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.02149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd2f057d09272a5877752aeb68e4bea7f8d98e6aad48a86159b519c3d2375c38","sha256:5104c63416121cb50211801917f297afe63acb23eec6021de03b209537454727"],"state_sha256":"3bcad5a9f1bf2199877e3f28a870decb45c461b72ef4cd8341ecd6f844d27554"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJ8Xd2Q5NiRDFFKi2u9JskPqzQtvIG3LnIW7XHfat+ZahXaSLSmfSiuNphj3/RpEF2rNs39QYgeg+Mg5wKYQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:28:34.077273Z","bundle_sha256":"3e894d37f37bac7f09cf1814cf0e28cadcd6aeb19023d3c1bd7154b799565c6a"}}