{"paper":{"title":"Generalized Fine-Tuning of Diffusion Models via Stochastic Control and FBSDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OC","authors_text":"Lu Wang, Zirui Wang","submitted_at":"2026-06-28T09:24:19Z","abstract_excerpt":"We propose a generalized fine-tuning framework for diffusion models from the perspective of stochastic control. Beyond entropy-regularized formulations, we introduce a general running cost that induces a relative generalized path cost, encompassing both Kullback-Leibler divergence and optimal transport metrics as special cases. This leads to a fully nonlinear Hamilton-Jacobi-Bellman equation. We characterize the value function through a forward-backward stochastic differential equation system and establish existence and uniqueness under standard regularity conditions. The optimal control admit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22660","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22660/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}