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We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $\\sigma^2 \\mapsto \\kappa(\\sigma^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \\textit{anisotropy} across eigenmodes, \\textit{inhomogeneity} across inputs, and over","title":"A Random Matrix Theory Perspective on the Consistency of Diffusion Models","url":"https://arxiv.org/abs/2602.02908","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.02908v2 Announce Type: replace-cross \nAbstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. 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For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \\textit{anisotropy} across eigenmodes, \\textit{inhomogeneity} across inputs, and over","title":"A Random Matrix Theory Perspective on the Consistency of Diffusion Models","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/2602.02908"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f0b5fabef88696e3484da996399e238e8e2c64589aa4b2526fb5bac503fba0d5e2d8065a694e02a0b6c36ee3dd26e52fc47c743fb87d9e613744ab962b196309","signer":"crovia.substrate","subject":{"observed_at":"2026-07-07T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2602.02908"},"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":"ce5c2bc44361403f46252130e3ae1ba191617c2b8cd1bf2cbd07c7eaf158344f","leaf_index":289351,"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":"d052d4e0d310e469b6efddf6d7e32c713a79d668bc183ed9f1caebd19983de3b","side":"left"},{"sibling":"6a268a72564b6a323b57d253ac5ede259e2d0a84548a748049668aea5e21a3b8","side":"left"},{"sibling":"c499578a8350803d258e1c840c8121d16b2885d0c7e69fadc102c55f48285d6d","side":"left"},{"sibling":"da5ba3590a3b7ccfff5914b1d7744b7640011a18fd6e75d9502e704d695546b5","side":"right"},{"sibling":"6157d24c9dd4d138e58cb0415ded54171907591b297f4ee56958ac7b634e21a8","side":"right"},{"sibling":"b4b3fdb042b5e716a678771ca7ab4b0d4901f1c0adfb80037dba93bd66a0d3a6","side":"right"},{"sibling":"267dd112e674315ecd9b3cbdd934dbc9d6f83a3dd743947e87095d624b0d5d16","side":"left"},{"sibling":"5adcd5a480e23093dce11f4b3900b046cf6185bd037ccd9881856faa29f08083","side":"right"},{"sibling":"f6a26c200957df5b056969d2ac473b7e794709bf54454460f447a4af62c6bd58","side":"right"},{"sibling":"c6f2478caecaf381e6b06b04f99195339b88d0db4da957bf2106979ee4a0375c","side":"left"},{"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_fc21e07bdaa8f50f597f611a95d6d70e6cd3fee7aca9c5e8ed9e332a084a7fa5"}}