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However, these models are typically deterministic, which makes them difficult to optimize with reinforcement learning (RL) post-training methods that require stochastic trajectories and well-defined likelihood ratios. Existing SDE-based stochasticization techniques are designed for velocity-based samplers with infinitesimal or finely discretized transitions, and therefore do not directly apply to long-range flow maps. In this work, we propose Flow-Map GRPO, an online RL post-training framework for deterministic few-step flow-map generators. The key component is Anchored Stochastic Flow Map Composition (ASFMC), a path-preserving stochasticization mechanism that introduces randomness through anchor-based conditional resampling while preserving the original marginal probability p","title":"Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition","url":"https://arxiv.org/abs/2607.00535","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.00535v1 Announce Type: cross \nAbstract: Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data. However, these models are typically deterministic, which makes them difficult to optimize with reinforcement learning (RL) post-training methods that require stochastic trajectories and well-defined likelihood ratios. Existing SDE-based stochasticization techniques are designed for velocity-based samplers with infinitesimal or finely discretized transitions, and therefore do not directly apply to long-range flow maps. In this work, we propose Flow-Map GRPO, an online RL post-training framework for deterministic few-step flow-map generators. The key component is Anchored Stochastic Flow Map Composition (ASFMC), a path-preserving stochasticization mechanism that introduces randomness through anchor-based conditional resampling while preserving the original marginal probability p","title":"Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-02T04:43:28Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.00535"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:a209accc3eba3585d1f0e8c64fcc4eefb0785366b0fa3c8868b731adb4b7e3cbe5bb7ec9022d7edffbe91c2bf1e9685b209c8dc66efcb06575c901acae331c0b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-02T04:43:28Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.00535"},"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":"e5777a27f5bd981922b8c48d0fd550e08efac07933d8d10567e66ade95d5aac2","leaf_index":272030,"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":"136bb3fe355d7bb61fc8b303b82d173438f0082b96569e77df7cb40aa356ca5e","side":"right"},{"sibling":"55f3c87f3bb39925793fae42d9ee267ff0068a82e09580f3da55ec2ff4029b18","side":"left"},{"sibling":"cb8d8e5d204e12e2c773ef4455872b97d60dddd7cf876584135fe1986ecdf5d9","side":"left"},{"sibling":"025ae062dcfaf937bde8f4f2143cc1a87549fea0dd04a0075328b512f39f4ed4","side":"left"},{"sibling":"244eca740c3a2e173a999cec255e6b2b3374e31caeec450f6581a8a1492da14d","side":"left"},{"sibling":"5709899a64d996ba122f54d3d2e1eadfb14fdf09e3611b9e2ef9273c8b88f0b0","side":"right"},{"sibling":"fb20322888e405335fce4284c86a4bf0c12c4d6bc87c0453f3c09ad3354c7e5c","side":"right"},{"sibling":"940858731d5be758fd8a2eb1da57b23657abab31e76c3d2d4ca6f9ae60489517","side":"left"},{"sibling":"155ae596a5c6a5260be50ff412642fbd25f4587b43e04c56950c1dc544719be1","side":"right"},{"sibling":"4cfdd7f7072619c015edc477162c2cf29c6f70370acb8dbddf1eb590876d82fe","side":"left"},{"sibling":"43990c9db8fcb3172d821965dfac69152981af4108b8dc87bd32f15c0e56f4cf","side":"left"},{"sibling":"15dbacc2e5845fe3bb835797bb7647ab6f091e79adadd39f40c636980716c622","side":"right"},{"sibling":"7ecc1d0d471643b88d886db58cb02a77af4d1495674760c3867834550b143757","side":"right"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"7b681d50e7d0a7b8d2a749507aed58030072539a90fab18de4f698743685cc00","side":"right"},{"sibling":"9b262645232510ff15bb7325ab858256f2914f711d2726caeafd49f5ca0fb7a9","side":"right"},{"sibling":"5bd94446b5721b713c5e4dcf4624b9bc682657ab2784af927caae7b80c297d7d","side":"right"},{"sibling":"21ac0b7091fe1133859bcd17b4f8da2fe37a2489d472dad508305740b483221b","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":272319,"merkle_root":"dd4fa4deb1f207e8a7756821b4f940f39e9f06a25e6fa8500a21dd403318a5a7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260702T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-02T05:38:06Z","sig_algorithm":"ed25519","signature":"68eb2e3bbc0f593bea7b5c3c110c90b6f4fe4fd8277d8dee7c866ba0471c1a50684aa4539c8a493e6d9c9202d8c03f4d897a0df3477e9ecd5b0ff03eb1016f00","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_003567c3ff083a521a9ff2f48fc3a948b9529663114d7f8c0bb209031f419b0f"}}