{"paper":{"title":"Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Atsushi Nitanda, Guoji Fu, Taiji Suzuki, Wee Sun Lee","submitted_at":"2026-05-15T10:20:05Z","abstract_excerpt":"Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\\mathcal{M} \\subset [0,1]^D$ with $d > 2$ and $\\beta$-H\\\"older densities strictly positive on $\\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein--1 sample exponent $\\tilde{\\mathcal{O}}(D^{\\mathcal{O}_\\beta(d)}n^{-(\\beta+1)/(d+2\\beta)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15822","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/2605.15822/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.724070Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.871203Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d97cbf7e95ab7794ab93601a619062b4da3b095317ee37d5962d1cfdcedc76ee"},"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"}