{"paper":{"title":"Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Heavy-tailed noise makes statistical estimation harder in diffusion models than Gaussian noise.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Antonio Ocello, Hamza Cherkaoui, H\\'el\\`ene Halconruy","submitted_at":"2026-05-13T08:37:59Z","abstract_excerpt":"Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is intuitive: if the data are heavy-tailed, HT noise may appear better matched than light-tailed (LT) Gaussian noise. However, replacing Gaussian noise by HT noise also changes the underlying estimation problem. In this paper, we revisit this paradigm through a combined theoretical and empirical study, establishing sampling-error bounds for two representative d"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the derived sampling-error bounds for the two representative diffusion models are tight enough to reflect practical performance differences between HT and LT noise across the tested regimes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Heavy-tailed noise in diffusion models leads to less favorable sampling-error bounds than light-tailed Gaussian noise by making the underlying statistical estimation problem harder.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Heavy-tailed noise makes statistical estimation harder in diffusion models than Gaussian noise.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"384378a8dde9f257125ea9755595684e37547bf170fffd90e0b5e784cc8c7c53"},"source":{"id":"2605.13175","kind":"arxiv","version":1},"verdict":{"id":"be39c0f9-5f95-4946-97f3-6e8b52e47314","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:07:39.988222Z","strongest_claim":"We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds.","one_line_summary":"Heavy-tailed noise in diffusion models leads to less favorable sampling-error bounds than light-tailed Gaussian noise by making the underlying statistical estimation problem harder.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the derived sampling-error bounds for the two representative diffusion models are tight enough to reflect practical performance differences between HT and LT noise across the tested regimes.","pith_extraction_headline":"Heavy-tailed noise makes statistical estimation harder in diffusion models than Gaussian noise."},"references":{"count":15,"sample":[{"doi":"","year":null,"title":"Initialization-aware score-based diffusion sampling.arXiv preprint arXiv:2603.00772,","work_id":"fe0b9c84-3c6b-4130-9088-13ad868bd075","ref_index":1,"cited_arxiv_id":"2603.00772","is_internal_anchor":true},{"doi":"","year":null,"title":"Diffusion generative models meet compressed sensing, with applications to imaging and finance.arXiv preprint arXiv:2509.03898,","work_id":"98b0239a-3092-41f2-9051-bef7217df386","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-3-030-52915-4","year":null,"title":"Springer Series in Operations Research and Financial Engineering","work_id":"1dc631c0-8b4f-44e0-8e51-1dd71862305c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Heavy-tailed diffusion with denoising lévy probabilistic models","work_id":"f1716af4-56e8-4ead-a5ec-365690f50fac","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities","work_id":"4fb70106-c9d6-48e2-9be8-707e4273105e","ref_index":5,"cited_arxiv_id":"2604.06065","is_internal_anchor":true}],"resolved_work":15,"snapshot_sha256":"63a28508f3e127f57b60a157be34b2d2de9ae603f5a066d37730c8ce629d938f","internal_anchors":2},"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"}