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Recent permutation diffusion methods define forward noising via shuffle-based random walks (e.g., riffle shuffles) and learn reverse transitions with Plackett-Luce (PL) variants, but the resulting trajectories can be abrupt and increasingly hard to denoise as n grows. We propose Soft-Rank Diffusion, a discrete diffusion framework that replaces shuffle-based corruption with a structured soft-rank forward process: we lift permutations to a continuous latent representation of order by relaxing discrete ranks into soft ranks, yielding smoother and more tractable trajectories. For the reverse process, we introduce contextualized generalized Plackett-Luce (cGPL) denoisers that generalize prior PL-style parameterizations and im","title":"Learning Permutation Distributions via Reflected Diffusion on Ranks","url":"https://arxiv.org/abs/2603.17353","vendor":"arxiv_cs_ai"},"summary":"arXiv:2603.17353v2 Announce Type: replace-cross \nAbstract: The finite symmetric group S_n provides a natural domain for permutations, yet learning probability distributions on S_n is challenging due to its factorially growing size and discrete, non-Euclidean structure. Recent permutation diffusion methods define forward noising via shuffle-based random walks (e.g., riffle shuffles) and learn reverse transitions with Plackett-Luce (PL) variants, but the resulting trajectories can be abrupt and increasingly hard to denoise as n grows. We propose Soft-Rank Diffusion, a discrete diffusion framework that replaces shuffle-based corruption with a structured soft-rank forward process: we lift permutations to a continuous latent representation of order by relaxing discrete ranks into soft ranks, yielding smoother and more tractable trajectories. For the reverse process, we introduce contextualized generalized Plackett-Luce (cGPL) denoisers that generalize prior PL-style parameterizations and im","title":"Learning Permutation Distributions via Reflected Diffusion on Ranks","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-16T04:43:43Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2603.17353"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c257cc30f67a3b0e5b36ecb8959aade85ad4962cadcda880fc6454ea29ee1f61c7480e098e95cf1d611c64be71e07dbf000527a2d511c7bedc3b2c031fa72309","signer":"crovia.substrate","subject":{"observed_at":"2026-06-16T04:43:43Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2603.17353"},"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":"62a2aa0f3d09272ac71559c94c40817d1d2eee301e9a5ed7020ec5b2764ce683","leaf_index":230759,"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":"db3ed91fc5f1d83a271ff0d53421ff0b13ff53f672ee57c6a84418421cc144e6","side":"left"},{"sibling":"98ff0282463c79b2ead2b1b7578e47edb5615e6542936c2e52155889c0a70aea","side":"left"},{"sibling":"67db1a7c99b436974708729ce35abe274558aee234089faad3510f0e958cfc2f","side":"left"},{"sibling":"d67b6977338ab420789bf410f9039d8a55894938a83843c1256c810a7ef292db","side":"right"},{"sibling":"637841f55270b1c076d4704fe1159baabbf2be395fcb12ed4c7d5a202ffb58ef","side":"right"},{"sibling":"7aa99f4015dd98a0563d2e83c85dcca08e69f45621f90f181a6cfdfc410f527c","side":"left"},{"sibling":"b1e1df12b4e8ce1b08b9338eb3b267a37cae01cbfb702d871739c875eda9aed2","side":"left"},{"sibling":"7a295c86e2ca5719bf2e33d1fcc4bc631f05c6f31aeb907113e2c58401e3087c","side":"right"},{"sibling":"ee59602dad0bf74c97a32a93f0a1a19e7a12f2800791988a6fdf35611febe031","side":"left"},{"sibling":"0c5669692381d605223c74b8d30f70cd308e77e33d5e40ea84bb7b4f84f2d4d9","side":"right"},{"sibling":"d5b9f8b1a2c9f6a46e17982dfbe6ce1f3b5fa4e730220397f2253d114dcc8486","side":"left"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_3ffc6fa8acecdd27ce0cc0f635b2402c3a50b24b689355552deceff3d08107c1"}}