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At the level of jump rates, these are one object in different coordinates, and reading a neural network in the wrong coordinate changes the process being trained and sampled. Starting with a rigorous derivation of the continuous-time Markov chain (CTMC) ELBO for any noising process, boundary terms included, we prove the \\emph{Oracle Distance} theorem: the negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one, not merely a bound. Its unique optimizer is therefore the conditional expectation of the true reverse jump rate given the current noisy state, and its irreducible cost is the rate at which the forward process $Z_t$ destroys information about the clean data $Z_0$, $-\\tfrac{d}{dt}I(Z_0; Z_t)$, so every noising process shares the same best achievable negative ELBO: the ","title":"What Does a Discrete Diffusion Model Learn?","url":"https://arxiv.org/abs/2607.05381","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.05381v1 Announce Type: cross \nAbstract: What does a discrete diffusion model learn: a denoiser, a score ratio, or a bridge plug-in predictor? At the level of jump rates, these are one object in different coordinates, and reading a neural network in the wrong coordinate changes the process being trained and sampled. Starting with a rigorous derivation of the continuous-time Markov chain (CTMC) ELBO for any noising process, boundary terms included, we prove the \\emph{Oracle Distance} theorem: the negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one, not merely a bound. Its unique optimizer is therefore the conditional expectation of the true reverse jump rate given the current noisy state, and its irreducible cost is the rate at which the forward process $Z_t$ destroys information about the clean data $Z_0$, $-\\tfrac{d}{dt}I(Z_0; Z_t)$, so every noising process shares the same best achievable negative ELBO: the ","title":"What Does a Discrete Diffusion Model Learn?","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-07T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.05381"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0e737bbcf534ca45af297da88fc4574f0ca86d9fa9a32c5900b65e30b8a1064b8619e4b753595811c9320e3511a387fddef0120a6d1ace96f0142d083928f806","signer":"crovia.substrate","subject":{"observed_at":"2026-07-07T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.05381"},"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":"109a9a63686dab9edc0b6face1f113acd07dc91d50603f507525bbf4afa31651","leaf_index":289157,"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":"cf0cd77b1be15c3c9fba544c46dd67ef8a5dfa0b3eceb450247d3c9acfe8ce7a","side":"left"},{"sibling":"737aebf2d5d1c4bac4fbd14998629081bf4b4993fbc5c82b45c48096600a5ae5","side":"right"},{"sibling":"2467441ee044c958414565bc22ac730acd01faf2380f4675c52cda69c7a6938f","side":"left"},{"sibling":"23625c70af7b8ac3cdd335c62d5accd86a35d14f774234a580ee1a89d95e2eb5","side":"right"},{"sibling":"fb1dd078d487e954c1b3ba0a9b05a73fbfb563777928c60e8348e9934385d9b2","side":"right"},{"sibling":"5d89f664a906e8defe2abbe89c134df0a9bc15697f6b1ab4c1f1a61ad5a75bdf","side":"right"},{"sibling":"cfebf4e758f80b6c0a2520ffba9d9d900a232da3623a4c530a1c712d33cffc24","side":"right"},{"sibling":"a6e115fb6d42f8f126d042702270c371c7df6161120ef9b37366edddc165bd28","side":"left"},{"sibling":"35d3e8088ee93171aa479055dcd001cfb6d23925114ddc0908531e54298b0d29","side":"left"},{"sibling":"841129c21a7583176cdc7de281cadfe0e00d04673461e199760cd5128d8cc2d5","side":"right"},{"sibling":"19d6dfd29bc47f35fa02e8fe765277ba9cc3e6da5072309f24ebaac5b5f295e3","side":"right"},{"sibling":"8e0ad7889eb2d4b40e5b6c3d8e2eb19d4e202374983f468aa76321823de07a9f","side":"left"},{"sibling":"aae716235efcb893a1f219dbcd5095070d08a497769fc6d50c14976aa26d5750","side":"right"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"1b72ad8d12164fdf329e7871711be99d8569d140b21f94056e6962da21da9ce1","side":"right"},{"sibling":"5f5109c2bfdcc7a7e70554bba25862e2d7ce86b6b0cd48a72eb66d2eb735f321","side":"right"},{"sibling":"05fd8a05dddb2e7f72bbb5b290ca55c378f1aed709f132277908d9a5f30eb605","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":289613,"merkle_root":"dc428b9d9ba248d4f93f63147bf7c700bf5be7f500cec6c3507b9df6e9401601","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260707T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-07T05:38:15Z","sig_algorithm":"ed25519","signature":"c468b0e183383ab71992be40bda451093e6cd8cd8efb0d26f68e135a804b287c209d12a0f4fdd95c69c835c04b78df8cb1903dee1f53d4730b36f5332a29fe05","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_fcd4585cbfa771b90920cb4c15caefdc91dcddf0c79e9ecee77c536f06ef1019"}}