{"paper":{"title":"Generalization bounds for score-based generative models: a synthetic proof","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arthur St\\'ephanovitch, Cl\\'ement Levrard, Eddie Aamari","submitted_at":"2025-07-07T09:13:09Z","abstract_excerpt":"We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\\star$ lies in a nonparametric $\\beta$-smooth H\\\"older class with either compact support or subGaussian tails on $\\mathbb{R}^d$, we prove that neural network-based score estimators trained via denoising score matching yield generative models achieving rate $n^{-(\\beta+1)/(2\\beta+d)}$ up to polylogarithmic factors. Our unified analysis handles arbitrary smoothness $\\beta > 0$, supports both deterministic and stochastic samplers, and leverages shape c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04794","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/2507.04794/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"}