{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:2TC2OEGXWARIXFIOLCXMBICLC7","short_pith_number":"pith:2TC2OEGX","canonical_record":{"source":{"id":"2212.06359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-13T03:48:01Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"title_canon_sha256":"8efadec9c3c340ad4d94f4c8882a2df92915e15409939ad82c23736deb41387f","abstract_canon_sha256":"43c46e6923b3896ad8c0e40a242727aaf1051dcd40e6e514bb52340687044bf4"},"schema_version":"1.0"},"canonical_sha256":"d4c5a710d7b0228b950e58aec0a04b17d4b5bcc6b36884f9fead9ad2640ac234","source":{"kind":"arxiv","id":"2212.06359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.06359","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"arxiv_version","alias_value":"2212.06359v1","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.06359","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_12","alias_value":"2TC2OEGXWARI","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_16","alias_value":"2TC2OEGXWARIXFIO","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_8","alias_value":"2TC2OEGX","created_at":"2026-07-05T05:24:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:2TC2OEGXWARIXFIOLCXMBICLC7","target":"record","payload":{"canonical_record":{"source":{"id":"2212.06359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-13T03:48:01Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"title_canon_sha256":"8efadec9c3c340ad4d94f4c8882a2df92915e15409939ad82c23736deb41387f","abstract_canon_sha256":"43c46e6923b3896ad8c0e40a242727aaf1051dcd40e6e514bb52340687044bf4"},"schema_version":"1.0"},"canonical_sha256":"d4c5a710d7b0228b950e58aec0a04b17d4b5bcc6b36884f9fead9ad2640ac234","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:24:49.373501Z","signature_b64":"WNI7mAcShbfhQ7otR5X1naTUV/AnPHvm16WSbJw0orrTSQBczCxRDBmejyRbRGHiEf2BXi6TRQI/UA7bkCHwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4c5a710d7b0228b950e58aec0a04b17d4b5bcc6b36884f9fead9ad2640ac234","last_reissued_at":"2026-07-05T05:24:49.373020Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:24:49.373020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.06359","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:24:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"95SgXJ9fx8A/450BvmuSHvP5vhD+m85j2bBZWAhCoEtyetbGaG/Y8S7PQBaGig/vxzDF413Mv6W5cDRc5ZheCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T13:14:53.125924Z"},"content_sha256":"d25c207d813a49204b8eb93e17ea1a21d6e53cc8d3567ddef962e73797610412","schema_version":"1.0","event_id":"sha256:d25c207d813a49204b8eb93e17ea1a21d6e53cc8d3567ddef962e73797610412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:2TC2OEGXWARIXFIOLCXMBICLC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Dohyun Kwon, Kangwook Lee, Ying Fan","submitted_at":"2022-12-13T03:48:01Z","abstract_excerpt":"Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still incomplete. Recently, Song et al. showed that the training objective of score-based generative models is equivalent to minimizing the Kullback-Leibler divergence of the generated distribution from the data distribution. In this work, we show that score-based models also minimize the Wasserstein distance between them under suitable assumptions on the model. Specific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06359","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/2212.06359/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":"2026-07-05T05:24:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NotVE6/QO/wOd10NW1tBYM2ritBdr9ilw8Lbb67a075uhxA+LTwS0BzqNcX4vPMIG0T1IEdIa+zkOS7wQZIOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-15T13:14:53.126307Z"},"content_sha256":"3e14793cce3f1e8ea2cccee177ba8f4288dd53346550f773de87ce3f5cabb97d","schema_version":"1.0","event_id":"sha256:3e14793cce3f1e8ea2cccee177ba8f4288dd53346550f773de87ce3f5cabb97d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TC2OEGXWARIXFIOLCXMBICLC7/bundle.json","state_url":"https://pith.science/pith/2TC2OEGXWARIXFIOLCXMBICLC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TC2OEGXWARIXFIOLCXMBICLC7/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":"2026-07-15T13:14:53Z","links":{"resolver":"https://pith.science/pith/2TC2OEGXWARIXFIOLCXMBICLC7","bundle":"https://pith.science/pith/2TC2OEGXWARIXFIOLCXMBICLC7/bundle.json","state":"https://pith.science/pith/2TC2OEGXWARIXFIOLCXMBICLC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TC2OEGXWARIXFIOLCXMBICLC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2TC2OEGXWARIXFIOLCXMBICLC7","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":"43c46e6923b3896ad8c0e40a242727aaf1051dcd40e6e514bb52340687044bf4","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-13T03:48:01Z","title_canon_sha256":"8efadec9c3c340ad4d94f4c8882a2df92915e15409939ad82c23736deb41387f"},"schema_version":"1.0","source":{"id":"2212.06359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.06359","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"arxiv_version","alias_value":"2212.06359v1","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.06359","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_12","alias_value":"2TC2OEGXWARI","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_16","alias_value":"2TC2OEGXWARIXFIO","created_at":"2026-07-05T05:24:49Z"},{"alias_kind":"pith_short_8","alias_value":"2TC2OEGX","created_at":"2026-07-05T05:24:49Z"}],"graph_snapshots":[{"event_id":"sha256:3e14793cce3f1e8ea2cccee177ba8f4288dd53346550f773de87ce3f5cabb97d","target":"graph","created_at":"2026-07-05T05:24:49Z","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/2212.06359/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still incomplete. Recently, Song et al. showed that the training objective of score-based generative models is equivalent to minimizing the Kullback-Leibler divergence of the generated distribution from the data distribution. In this work, we show that score-based models also minimize the Wasserstein distance between them under suitable assumptions on the model. Specific","authors_text":"Dohyun Kwon, Kangwook Lee, Ying Fan","cross_cats":["cs.AI","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-13T03:48:01Z","title":"Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06359","kind":"arxiv","version":1},"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:d25c207d813a49204b8eb93e17ea1a21d6e53cc8d3567ddef962e73797610412","target":"record","created_at":"2026-07-05T05:24:49Z","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":"43c46e6923b3896ad8c0e40a242727aaf1051dcd40e6e514bb52340687044bf4","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-13T03:48:01Z","title_canon_sha256":"8efadec9c3c340ad4d94f4c8882a2df92915e15409939ad82c23736deb41387f"},"schema_version":"1.0","source":{"id":"2212.06359","kind":"arxiv","version":1}},"canonical_sha256":"d4c5a710d7b0228b950e58aec0a04b17d4b5bcc6b36884f9fead9ad2640ac234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4c5a710d7b0228b950e58aec0a04b17d4b5bcc6b36884f9fead9ad2640ac234","first_computed_at":"2026-07-05T05:24:49.373020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:24:49.373020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WNI7mAcShbfhQ7otR5X1naTUV/AnPHvm16WSbJw0orrTSQBczCxRDBmejyRbRGHiEf2BXi6TRQI/UA7bkCHwCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:24:49.373501Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.06359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d25c207d813a49204b8eb93e17ea1a21d6e53cc8d3567ddef962e73797610412","sha256:3e14793cce3f1e8ea2cccee177ba8f4288dd53346550f773de87ce3f5cabb97d"],"state_sha256":"be66c67d52483348827a3bc5b4d323c76a8c7c43a10a87160c5f6d2342569f7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WIS7edduJ0uqky1XkvAX0HIibyFubqUxbUQ2jMAsc70TM+kHM5CN68AG9l1pFFj4vCnR6K3HMmrREN8GfIoHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-15T13:14:53.128863Z","bundle_sha256":"3c916212be459738389384b67c3187151e19857dfe7b54c0b24e29487662cf46"}}