{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:UGZBVFKSQ5JL7QRKP3S2EV32SG","short_pith_number":"pith:UGZBVFKS","schema_version":"1.0","canonical_sha256":"a1b21a95528752bfc22a7ee5a2577a91bd16beee3ffc2b2700dea23d9b481d73","source":{"kind":"arxiv","id":"2211.01364","version":3},"attestation_state":"computed","paper":{"title":"An optimal control perspective on diffusion-based generative modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Julius Berner, Karen Ullrich, Lorenz Richter","submitted_at":"2022-11-02T17:59:09Z","abstract_excerpt":"We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.01364","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-11-02T17:59:09Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"54345a4e1f6ed804e33842636392c3064e93b1a601667ec4cfedbb5314f8cee0","abstract_canon_sha256":"8b382efeba7d2f0b9b8f7df769dcbccfc8fe19fcd74e118520b163866fd03ba4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:31.087576Z","signature_b64":"995ewOfQJfbAG+mG9GOQuuTlIAKIbhPzlbh8BB4dIZNKBzPasC196i9Un1k8TGFllwgM/6Qzh+wFITCnOB03Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1b21a95528752bfc22a7ee5a2577a91bd16beee3ffc2b2700dea23d9b481d73","last_reissued_at":"2026-07-05T08:00:31.087105Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:31.087105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An optimal control perspective on diffusion-based generative modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Julius Berner, Karen Ullrich, Lorenz Richter","submitted_at":"2022-11-02T17:59:09Z","abstract_excerpt":"We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.01364","kind":"arxiv","version":3},"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/2211.01364/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.01364","created_at":"2026-07-05T08:00:31.087161+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.01364v3","created_at":"2026-07-05T08:00:31.087161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.01364","created_at":"2026-07-05T08:00:31.087161+00:00"},{"alias_kind":"pith_short_12","alias_value":"UGZBVFKSQ5JL","created_at":"2026-07-05T08:00:31.087161+00:00"},{"alias_kind":"pith_short_16","alias_value":"UGZBVFKSQ5JL7QRK","created_at":"2026-07-05T08:00:31.087161+00:00"},{"alias_kind":"pith_short_8","alias_value":"UGZBVFKS","created_at":"2026-07-05T08:00:31.087161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":9,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.28785","citing_title":"Stochastic Optimal Control Sampling for Diffusion Inverse Problems","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2410.01244","citing_title":"Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16520","citing_title":"Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.08580","citing_title":"Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08928","citing_title":"Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00337","citing_title":"FES-FM: Free Energy Surface Sampling via Reduced Flow Matching","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10983","citing_title":"Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07762","citing_title":"Generative optimal transport via forward-backward HJB matching","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15576","citing_title":"Nonlinear Stochastic Density Steering via Gaussian Mixture Schrodinger Bridges and Multiple Linearizations","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG","json":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG.json","graph_json":"https://pith.science/api/pith-number/UGZBVFKSQ5JL7QRKP3S2EV32SG/graph.json","events_json":"https://pith.science/api/pith-number/UGZBVFKSQ5JL7QRKP3S2EV32SG/events.json","paper":"https://pith.science/paper/UGZBVFKS"},"agent_actions":{"view_html":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG","download_json":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG.json","view_paper":"https://pith.science/paper/UGZBVFKS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.01364&json=true","fetch_graph":"https://pith.science/api/pith-number/UGZBVFKSQ5JL7QRKP3S2EV32SG/graph.json","fetch_events":"https://pith.science/api/pith-number/UGZBVFKSQ5JL7QRKP3S2EV32SG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG/action/storage_attestation","attest_author":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG/action/author_attestation","sign_citation":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG/action/citation_signature","submit_replication":"https://pith.science/pith/UGZBVFKSQ5JL7QRKP3S2EV32SG/action/replication_record"}},"created_at":"2026-07-05T08:00:31.087161+00:00","updated_at":"2026-07-05T08:00:31.087161+00:00"}