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While Direct Preference Optimization offers a path to alignment, its reliance on spectrally flat Gaussian noise fails to distinguish authentic high-frequency details from hallucinations. To bridge this geometric gap, we propose ASASR, a theoretically grounded framework that recasts the generative flow into a Sobolev-induced Riemannian geometry by explicitly coloring the noise transition kernel to mirror natural spectral decay. Driving this geometric alignment, we integrate a parametric adversary grounded in the Riesz Representation Theorem, which synthesizes targeted negative samples equivalent to worst-case Sobolev gradients to direct optimization along the tangent space of plausible structural failures.","title":"Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution","url":"https://arxiv.org/abs/2605.23264","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.23264v2 Announce Type: replace-cross \nAbstract: Generative priors in Image Super-Resolution (SR) often compromise faithful restoration, we attribute this limitation to a fundamental spectral misalignment between isotropic objectives and the intrinsic natural image manifold. While Direct Preference Optimization offers a path to alignment, its reliance on spectrally flat Gaussian noise fails to distinguish authentic high-frequency details from hallucinations. 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Driving this geometric alignment, we integrate a parametric adversary grounded in the Riesz Representation Theorem, which synthesizes targeted negative samples equivalent to worst-case Sobolev gradients to direct optimization along the tangent space of plausible structural failures.","title":"Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-29T04:44:03Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.23264"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:dd5b7b74ce0bdceb19eafe1a6793f8c08e06e18dedfa59dc7e2881a98b8bed8fa1e3b5dbeb9eb766127703f79394d9931e063d82dfab94c5135ec5e5d560720e","signer":"crovia.substrate","subject":{"observed_at":"2026-06-29T04:44:03Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.23264"},"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":"ce926adbc29c801917d1056ecd01be5cbfd296a2d86676f57e59f2f9bdfeb47c","leaf_index":261527,"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":"1fc1648895ea4e624ace75f982c7ddef0806a09568d1c77bff1cd59d515a664c","side":"left"},{"sibling":"68d21b647d855e2b654468c1e0197df3126212c13e344aff49f2b127fb1ce6a9","side":"left"},{"sibling":"2ac2b883c758bf74be3013729f967a3353d11b90ecae456248a51ada885a686b","side":"left"},{"sibling":"7c706d26bea1c2f9a8ebd64953e875bee8b7019960d246522ed249efdd8f3059","side":"right"},{"sibling":"b34608b126aad530de8a3e3758a62fcd7852bc583fe7988cbd1d3c7a370666f9","side":"left"},{"sibling":"10c5a683549a2b5f04f99eb583a39ef678d0d07407d49815cc3568dd41933710","side":"right"},{"sibling":"68a8ff8f71247734930721fd8fb46d5601c2f438645b61686958db9f099baa00","side":"right"},{"sibling":"6541e04390f40ec94bca13a445548c91511634a5ffb1a1a6cce967da56056afd","side":"left"},{"sibling":"6d1df65d14253ed3a13c03e25aa9adcd9a091d8062a82e8586bcaee74013b90e","side":"left"},{"sibling":"9f9daa9d12e65b219f34c92aec45450536b79a42b8892050d66961432ae28ed1","side":"right"},{"sibling":"b5725d7b0807dc6da32d9788f20057fa8726be38d30a9ebdabc605ae92739122","side":"left"},{"sibling":"e321b2cac14cbe28f76ccb7938249a40ff60cd5d2128b5634be046ea10e984b8","side":"left"},{"sibling":"5900dc6c7d13855af9d0385baf1691ec386df33e450c422af1cabe0a36e40ad8","side":"left"},{"sibling":"ae636ddee98c71ab7a7dc55ddfab70c7f710a2b6abfdf7a8b5d16a4017d1c0d1","side":"left"},{"sibling":"f29798d8bb6aa9900eab878992d9ff0c53266debd87472f31ab26a6a3fb55880","side":"left"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"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":261662,"merkle_root":"aa8865c239aa2eb6c8aa7c6250f56b3cd5709854a8a07f6a29eb4ddd8802cb6f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260629T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-29T05:38:02Z","sig_algorithm":"ed25519","signature":"476329233e82fb35fba2552ddc5d1d75b2bdd8513bbd281e9c40a0b8e475df374a62dcd8b456b0c5e8815984f5b4bf0983ae95d2cf4d7412ebb13a433b933c0a","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_3eb17437fe0d9bcfb658228a90646b44a5ccc1e6318daf85c59a40c15372b7d2"}}