Pith Number

pith:VBA26UM7

pith:2026:VBA26UM7XKZYXG2D4HXYQW6JDQ

not attested not anchored not stored refs resolved

Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training

Antonio Ocello, Hamza Cherkaoui, H\'el\`ene Halconruy

Heavy-tailed noise makes statistical estimation harder in diffusion models than Gaussian noise.

arxiv:2605.13175 v1 · 2026-05-13 · cs.LG

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that HT noise makes the statistical estimation problem harder, leading to less favorable sampling-error bounds.

C2weakest 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.

C3one 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.

References

15 extracted · 15 resolved · 2 Pith anchors

[1] Initialization-aware score-based diffusion sampling.arXiv preprint arXiv:2603.00772, · arXiv:2603.00772

[2] Diffusion generative models meet compressed sensing, with applications to imaging and finance.arXiv preprint arXiv:2509.03898,

[3] Springer Series in Operations Research and Financial Engineering · doi:10.1007/978-3-030-52915-4

[4] Heavy-tailed diffusion with denoising lévy probabilistic models 2025

[5] Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities · arXiv:2604.06065

Receipt and verification

First computed	2026-05-18T03:08:56.485470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a841af519fbab38b9b43e1ef885bc91c0b29086f5669175c1ffe955d5d9952b7

Aliases

arxiv: 2605.13175 · arxiv_version: 2605.13175v1 · doi: 10.48550/arxiv.2605.13175 · pith_short_12: VBA26UM7XKZY · pith_short_16: VBA26UM7XKZYXG2D · pith_short_8: VBA26UM7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VBA26UM7XKZYXG2D4HXYQW6JDQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a841af519fbab38b9b43e1ef885bc91c0b29086f5669175c1ffe955d5d9952b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "112280043ddbcafb9f0b569126ba471a7d61a44638d7c5da1ea8ff3b70772e88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T08:37:59Z",
    "title_canon_sha256": "767685429e53469c55d11cbbbfb667cad6f9e6cc26032a48ac1876b5628df505"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13175",
    "kind": "arxiv",
    "version": 1
  }
}