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Motivated by privacy and scalability, recent decentralized diffusion architectures replace a single global velocity field with multiple local experts and a routing mechanism, yielding a sampling dynamics with stochastic expert switching that falls outside standard diffusion convergence analyses. In this work, We study a decentralized diffusion framework with stochastic velocity fields and ODE-based sampling. We establish a convergence guarantee in Wasserstein-2 distance, showing that the distribution of the $N$-step discretization converges to the analytical solution at rate $\\mathcal{O}(N^{-1/2}+\\varepsilon)$ in $W_2$, where $\\varepsilon$ captures the neural approximation errors. To our knowledge, this is the first $W_2$ convergence result for decentralized diffusion models with an ODE-based ","title":"Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition","url":"https://arxiv.org/abs/2606.15835","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.15835v1 Announce Type: cross \nAbstract: Diffusion models have achieved impressive empirical success in generative tasks, and their convergence theory is now relatively well understood. Motivated by privacy and scalability, recent decentralized diffusion architectures replace a single global velocity field with multiple local experts and a routing mechanism, yielding a sampling dynamics with stochastic expert switching that falls outside standard diffusion convergence analyses. In this work, We study a decentralized diffusion framework with stochastic velocity fields and ODE-based sampling. We establish a convergence guarantee in Wasserstein-2 distance, showing that the distribution of the $N$-step discretization converges to the analytical solution at rate $\\mathcal{O}(N^{-1/2}+\\varepsilon)$ in $W_2$, where $\\varepsilon$ captures the neural approximation errors. To our knowledge, this is the first $W_2$ convergence result for decentralized diffusion models with an ODE-based ","title":"Wasserstein Convergence of ODE-Based Samplers in Decentralized Diffusion Model via Velocity Field Decomposition","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/2606.15835"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c17715ac2a593a2ffb5ec32eded14e7417b6577031f540b17419e470820b2cd616b8d23572e82e0a2197722c60662be0be6d2763b3937d7a830baf38d87ba603","signer":"crovia.substrate","subject":{"observed_at":"2026-06-16T04:43:43Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.15835"},"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":"89e80e8b3c986188e2bb24fac3a9f9a4157dfa8aa372547513dc1da3f7f64d53","leaf_index":230476,"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":"2163a4bfe4ff87925eb01976b75426b87b7a52ccdbb228a80b83125131611b87","side":"right"},{"sibling":"c9722c1cb37cea962e49418663a55c8bbf7a5a86a8da3518bdefb0270cb482e8","side":"right"},{"sibling":"98a1ba8b902bff97e919b3b8e8747ae7e304ed423b425e93b4fbfbae0c2026e0","side":"left"},{"sibling":"1943deca40347de19d1c9c2851215beeebf26de641757ebe028fc40f5828b45f","side":"left"},{"sibling":"fdc2402e34bbead1124cafc562290c9f0976f26fca4ea77da0186d8b6595c045","side":"right"},{"sibling":"a6a4305ebc8fd938ec1067b5d8dddc092b9ee91eb9316c17b7fcd4d7c5ecc6a1","side":"right"},{"sibling":"96d9b7ee6d46d2c6d0078e6f6295557abfed0d62f449449bf4962d81989410dc","side":"left"},{"sibling":"5e70a98340dea4a4509e7050c42e3706fa23334d35ad282b0e9f997e7ba855f2","side":"right"},{"sibling":"63d6b9d8af7ae8348285d3493af29f64992ecec42f5f1cae99c8604cd1703487","side":"right"},{"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_b78bdc21ff4ee3b251b0a02d9b856e813f87373fb7f14ab7494c5da68d0e4f44"}}