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Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field \\(b_t\\) of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects: \\(b_t = u_t + d_t\\), where \\(u_t\\) governs marginal probability transport and \\(d_t\\) captures an osmotic effect induced by diffusion and determined b","title":"Deterministic Decomposition of Stochastic Generative Dynamics","url":"https://arxiv.org/abs/2605.08794","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.08794v2 Announce Type: replace-cross \nAbstract: Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field \\(b_t\\) of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects: \\(b_t = u_t + d_t\\), where \\(u_t\\) governs marginal probability transport and \\(d_t\\) captures an osmotic effect induced by diffusion and determined b","title":"Deterministic Decomposition of Stochastic Generative Dynamics","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-19T04:43:36Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.08794"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:65fe1bf3d13a151ae43ca54c3112826d042de171e32a28e2e733cc4b973c864881ffd45561bded152b676570cb0e71592771e5f3207eb15198256b2760d8a00b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-19T04:43:36Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.08794"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"fc4ca7518e0b8310127c2af262ceab49e759799af7ea948b579d2027d72be81a","leaf_index":143225,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"29c23784b1fd315d81acf70a85ee6de0c09377293b4d1a50a83b19c1565a316e","side":"left"},{"sibling":"a222265c347ad981ee0cb9b9e51fd115190e95fe98ad862eb9233e6b64b05958","side":"right"},{"sibling":"cf0bcf3c0c19e74f12154faa9e6485e481554d83f2973c45914ae3c18fffcb94","side":"right"},{"sibling":"f5451fc490c3a9b12f534dd25f0ac0ed9d033ad57eab2034ba0be178027a8e45","side":"left"},{"sibling":"e65147fa576fdf0cf2c8b9635bc736be38330b71d98dd6cc9b657767d741987a","side":"left"},{"sibling":"5dad6386ffb49e60936803c095332e0bc5865e7f3ca69e43f32881f4ec5bb7f2","side":"left"},{"sibling":"d1fb94274b8481dad6b8edcb50724352d9f6aa9e4c5ef7ad6392960664390822","side":"left"},{"sibling":"4b6dab10c74fb2a96436053a067988cc08e1b2f810f1362c194b7439e788d860","side":"right"},{"sibling":"b986468aca0b7804b8a608705cafc663139e79ff550a69be0b9dd58ec70714f7","side":"left"},{"sibling":"db97141c585f6a1e6bebe92b3ea300ea0f38a2321ca286d85850b11b2dd162a6","side":"left"},{"sibling":"202f1bead178ef3785968d50d3d188264a95192a077654c331612e04a34cbfbe","side":"left"},{"sibling":"72249c8c8b068386e35d16f4bd0bbeb9ba820ca217ef0f0d28396c9fe493f5f0","side":"left"},{"sibling":"ea64599340f7ffdf17ad0cbc1d9401ef8870a347e3847bdc106d06b1673df09c","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"4db1f363729507e27a60851cf6ed334d7b9acdef194ed7d419aba4d2bd367a4a","side":"right"},{"sibling":"a86ee18c45e7fcc408b6007eaece05aa75b2d9ae30252e9e878462b4dffbef7b","side":"right"},{"sibling":"1d18e7663d43ccff0122ecc7ee12645bb16afb607b218e81b1ea2408f863cb78","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":143302,"merkle_root":"999156d40a7c61d9ddd52b7338f3cbda3e68f53bace070c7b616ea194e23b123","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260519T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-19T05:37:30Z","sig_algorithm":"ed25519","signature":"b1a252cc66ff32bed1d10dd88a6b2a200e3856d3dbcfcc4ee55e02e00f3d548e854ed9c544704b222bd5d315492c4a935ba2d90d727c585a67899b0ad602fc05","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_51924f31f4e424e87abe2ca63daddf01c7d0b7871833a75ade76cd6272726969"}}