{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MGHMVQPECJN7HQMAFWJN42CLYP","short_pith_number":"pith:MGHMVQPE","canonical_record":{"source":{"id":"2208.07949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-16T21:18:31Z","cross_cats_sorted":[],"title_canon_sha256":"a745a3f9d54d6fd94b5efa63a914afe00317151ac09bf9043ca7cd34e8be6778","abstract_canon_sha256":"4254e57a06422800aca205c4caeb402f5f84befa36046fb2ad0affbb357c4727"},"schema_version":"1.0"},"canonical_sha256":"618ecac1e4125bf3c1802d92de684bc3d7159dc50ef3152bd1879279ec83c603","source":{"kind":"arxiv","id":"2208.07949","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07949","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07949v1","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07949","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"MGHMVQPECJN7","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"MGHMVQPECJN7HQMA","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"MGHMVQPE","created_at":"2026-07-05T04:49:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MGHMVQPECJN7HQMAFWJN42CLYP","target":"record","payload":{"canonical_record":{"source":{"id":"2208.07949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-16T21:18:31Z","cross_cats_sorted":[],"title_canon_sha256":"a745a3f9d54d6fd94b5efa63a914afe00317151ac09bf9043ca7cd34e8be6778","abstract_canon_sha256":"4254e57a06422800aca205c4caeb402f5f84befa36046fb2ad0affbb357c4727"},"schema_version":"1.0"},"canonical_sha256":"618ecac1e4125bf3c1802d92de684bc3d7159dc50ef3152bd1879279ec83c603","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:49:12.912725Z","signature_b64":"QW9FIw00zLX+gcIcW2DsLP7ERz18nq7qnzjUxkLSUXtZOWOMBrt0+Vyr8SXZATlx/lW7gu3ZtQ3KfUIUUQeaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"618ecac1e4125bf3c1802d92de684bc3d7159dc50ef3152bd1879279ec83c603","last_reissued_at":"2026-07-05T04:49:12.912408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:49:12.912408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.07949","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":"2026-07-05T04:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKit7ZROk8CikH6LdHaSYBKwPkvoj5fSzKh+ssYhF4xDHMcb+Wa3nTiFfH8O9VohZYy6K+yk0p01Du1ELgceBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:27:18.853721Z"},"content_sha256":"b42c76806bdd461b5eaa6a378cb68624a5f2b8c7f26d3526a785fedbed481e5d","schema_version":"1.0","event_id":"sha256:b42c76806bdd461b5eaa6a378cb68624a5f2b8c7f26d3526a785fedbed481e5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MGHMVQPECJN7HQMAFWJN42CLYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemannian Diffusion Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aaron Courville, Avishek Joey Bose, Chin-Wei Huang, Milad Aghajohari, Prakash Panangaden","submitted_at":"2022-08-16T21:18:31Z","abstract_excerpt":"Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed in the likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07949","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/2208.07949/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":"2026-07-05T04:49:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1SG/Gcj+W4XRGcTZ41IW9CsaA1YaqL7sT7xj/RzMMA2cbajVcALAQHqBV3jg43+HB7XAVnsbUu2ESq/LdprBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:27:18.854255Z"},"content_sha256":"8cbe858bbd873081e3b42b2cd11ab9e52e970288e04ad5da5f2eb5e520043d87","schema_version":"1.0","event_id":"sha256:8cbe858bbd873081e3b42b2cd11ab9e52e970288e04ad5da5f2eb5e520043d87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGHMVQPECJN7HQMAFWJN42CLYP/bundle.json","state_url":"https://pith.science/pith/MGHMVQPECJN7HQMAFWJN42CLYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGHMVQPECJN7HQMAFWJN42CLYP/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":"2026-08-04T19:27:18Z","links":{"resolver":"https://pith.science/pith/MGHMVQPECJN7HQMAFWJN42CLYP","bundle":"https://pith.science/pith/MGHMVQPECJN7HQMAFWJN42CLYP/bundle.json","state":"https://pith.science/pith/MGHMVQPECJN7HQMAFWJN42CLYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGHMVQPECJN7HQMAFWJN42CLYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MGHMVQPECJN7HQMAFWJN42CLYP","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":"4254e57a06422800aca205c4caeb402f5f84befa36046fb2ad0affbb357c4727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-16T21:18:31Z","title_canon_sha256":"a745a3f9d54d6fd94b5efa63a914afe00317151ac09bf9043ca7cd34e8be6778"},"schema_version":"1.0","source":{"id":"2208.07949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07949","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07949v1","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07949","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"MGHMVQPECJN7","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_16","alias_value":"MGHMVQPECJN7HQMA","created_at":"2026-07-05T04:49:12Z"},{"alias_kind":"pith_short_8","alias_value":"MGHMVQPE","created_at":"2026-07-05T04:49:12Z"}],"graph_snapshots":[{"event_id":"sha256:8cbe858bbd873081e3b42b2cd11ab9e52e970288e04ad5da5f2eb5e520043d87","target":"graph","created_at":"2026-07-05T04:49:12Z","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/2208.07949/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed in the likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion","authors_text":"Aaron Courville, Avishek Joey Bose, Chin-Wei Huang, Milad Aghajohari, Prakash Panangaden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-16T21:18:31Z","title":"Riemannian Diffusion Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07949","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:b42c76806bdd461b5eaa6a378cb68624a5f2b8c7f26d3526a785fedbed481e5d","target":"record","created_at":"2026-07-05T04:49:12Z","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":"4254e57a06422800aca205c4caeb402f5f84befa36046fb2ad0affbb357c4727","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-16T21:18:31Z","title_canon_sha256":"a745a3f9d54d6fd94b5efa63a914afe00317151ac09bf9043ca7cd34e8be6778"},"schema_version":"1.0","source":{"id":"2208.07949","kind":"arxiv","version":1}},"canonical_sha256":"618ecac1e4125bf3c1802d92de684bc3d7159dc50ef3152bd1879279ec83c603","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"618ecac1e4125bf3c1802d92de684bc3d7159dc50ef3152bd1879279ec83c603","first_computed_at":"2026-07-05T04:49:12.912408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:49:12.912408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QW9FIw00zLX+gcIcW2DsLP7ERz18nq7qnzjUxkLSUXtZOWOMBrt0+Vyr8SXZATlx/lW7gu3ZtQ3KfUIUUQeaCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:49:12.912725Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.07949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b42c76806bdd461b5eaa6a378cb68624a5f2b8c7f26d3526a785fedbed481e5d","sha256:8cbe858bbd873081e3b42b2cd11ab9e52e970288e04ad5da5f2eb5e520043d87"],"state_sha256":"1b5e61614761773c94618b504536196ddfc184e84cab4d074587b3799a23926b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ai4blJ9TuWod8HUYMlpFK4uj6HdjzJh3RQQr+mwwsncX/CE79cqzw28RTOezHqB2/MQ/Cv8tAD/rvulj29A/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:27:18.858869Z","bundle_sha256":"9c03ecb92ac85bc2537d2a49c58671955aca856eaf8c0780ddb6f85ffd1c49a5"}}