{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RFPFQ5EWG2XQCFWXY775R4ACSW","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":"fe235de2a7d02eea98f38937654208375c37cf2cee0afbb76e4982c7479021f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-30T12:34:16Z","title_canon_sha256":"790b7a64f630c7303b25786f6a7dc292cb2ada97ee7bd3ce216af470b1f9dcb4"},"schema_version":"1.0","source":{"id":"2606.31576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31576","created_at":"2026-07-01T01:18:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31576v1","created_at":"2026-07-01T01:18:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31576","created_at":"2026-07-01T01:18:08Z"},{"alias_kind":"pith_short_12","alias_value":"RFPFQ5EWG2XQ","created_at":"2026-07-01T01:18:08Z"},{"alias_kind":"pith_short_16","alias_value":"RFPFQ5EWG2XQCFWX","created_at":"2026-07-01T01:18:08Z"},{"alias_kind":"pith_short_8","alias_value":"RFPFQ5EW","created_at":"2026-07-01T01:18:08Z"}],"graph_snapshots":[{"event_id":"sha256:280a9154eeea0d9cfb5af3861500b060a2572e33e2e33331823941afef30d268","target":"graph","created_at":"2026-07-01T01:18:08Z","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/2606.31576/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The use of ordinary and stochastic differential equations has led to substantial progress in generative machine learning with applications to, for example, image, video and biomolecule generation. This paper provides a self-contained and informal introduction to the differential equations, the probabilistic framework for using them in generative modeling and the Fokker--Planck equation that governs the temporal evolution of the marginal distribution of the stochastic variables of the differential equations. The variational lower bound on the log-likelihood (the evidence lower bound, ELBO) is d","authors_text":"Andrea Dittadi, Andriy Mnih, Manfred Opper, Ole Winther, Paul Jeha, Sander Dieleman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-30T12:34:16Z","title":"Introduction to Stochastic Differential Equations for Generative Machine Learning: A Variational Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31576","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":"sha256:9b56e466df75cc4e6b29ae5d2bad8fcdd2327f7dc65397a1531bddde8e298f3e","target":"record","created_at":"2026-07-01T01:18:08Z","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":"fe235de2a7d02eea98f38937654208375c37cf2cee0afbb76e4982c7479021f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-30T12:34:16Z","title_canon_sha256":"790b7a64f630c7303b25786f6a7dc292cb2ada97ee7bd3ce216af470b1f9dcb4"},"schema_version":"1.0","source":{"id":"2606.31576","kind":"arxiv","version":1}},"canonical_sha256":"895e58749636af0116d7c7ffd8f0029584b67f339164c513fa73b375de285544","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"895e58749636af0116d7c7ffd8f0029584b67f339164c513fa73b375de285544","first_computed_at":"2026-07-01T01:18:08.159863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:18:08.159863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uc2q81lvrlV5nzzeRhW67jIWUlq3h5n98rOlun7Z2FFH0R6Dq+hvMIMYBgKdEzYN2Kyj8c1CL8ZhjS0K5q3wCg==","signature_status":"signed_v1","signed_at":"2026-07-01T01:18:08.160269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b56e466df75cc4e6b29ae5d2bad8fcdd2327f7dc65397a1531bddde8e298f3e","sha256:280a9154eeea0d9cfb5af3861500b060a2572e33e2e33331823941afef30d268"],"state_sha256":"4d0a8ea226f9f038833bbc4acc7f147b59034f41e4fa4ca496df2a55e36808af"}