Pith Number

pith:BIDBUGJO

pith:2026:BIDBUGJOSISRNGVTUCWCERJZEE

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Diffusion Processes on Implicit Manifolds

Adam Gosztolai, Clara Grotehans, Pierre Vandergheynst, Victor Kawasaki-Borruat

Point-cloud diffusions converge in law to their manifold counterparts as sample size increases.

arxiv:2604.07213 v2 · 2026-04-08 · cs.LG · math.PR

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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, as the number of samples grows, the induced process converges in law on the space of probability paths to its smooth manifold counterpart.

C2weakest assumption

The point cloud is sampled from a distribution supported near a smooth low-dimensional manifold, and the proximity graph built from the data sufficiently approximates the intrinsic geometry and diffusion operator on that manifold.

C3one line summary

Implicit Manifold-valued Diffusions (IMDs) are data-driven SDEs built from proximity graphs that converge in law to smooth manifold diffusions as sample count increases.

Formal links

2 machine-checked theorem links

Cited by

2 papers in Pith

Neural Point-Forms

Generative models on phase space

Receipt and verification

First computed	2026-05-21T01:05:18.684915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a061a192e9225169ab3a0ac2245392102d27807ef958cf6cd44e180b9ff8b62

Aliases

arxiv: 2604.07213 · arxiv_version: 2604.07213v2 · doi: 10.48550/arxiv.2604.07213 · pith_short_12: BIDBUGJOSISR · pith_short_16: BIDBUGJOSISRNGVT · pith_short_8: BIDBUGJO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BIDBUGJOSISRNGVTUCWCERJZEE \
  | 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: 0a061a192e9225169ab3a0ac2245392102d27807ef958cf6cd44e180b9ff8b62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1825f78f8d3f8fa0a9c9c5bf71aa4f12c2fec5323b512a61f5712445670690f0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-08T15:34:21Z",
    "title_canon_sha256": "2455bd6303c850c9fc4993c8f02e4eb009a9a9763e1923e57098deafdd334a47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07213",
    "kind": "arxiv",
    "version": 2
  }
}