Pith Number

pith:3MQ3NOMB

pith:2026:3MQ3NOMBXVOFH2ZP2NQ3JVYXBE

not attested not anchored not stored refs pending

Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching

Jian Wang, Jiarui Xing, Song Wang

For any pre-trained flow matching velocity field the trace of the posterior covariance equals the divergence of that field up to a time-dependent factor.

arxiv:2605.00941 v3 · 2026-05-01 · cs.LG · cs.CV

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\pithnumber{3MQ3NOMBXVOFH2ZP2NQ3JVYXBE}

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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

For any pre-trained flow matching velocity field, the trace of the posterior covariance over the clean data given the current state equals, in closed form, the divergence of the velocity field, up to a known time-dependent prefactor and an additive constant.

C2weakest assumption

The flow matching velocity field is assumed to be the exact conditional expectation under the posterior; any deviation from this (e.g., due to optimization error or model misspecification) would break the exact equality.

C3one line summary

In flow matching, the uncertainty of the clean data given the current state is exactly the divergence of the velocity field (up to a known scalar).

Receipt and verification

First computed	2026-05-22T01:04:03.975063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db21b6b981bd5c53eb2fd361b4d7170906a3097620b8cc7d1d705f69a69475fa

Aliases

arxiv: 2605.00941 · arxiv_version: 2605.00941v3 · doi: 10.48550/arxiv.2605.00941 · pith_short_12: 3MQ3NOMBXVOF · pith_short_16: 3MQ3NOMBXVOFH2ZP · pith_short_8: 3MQ3NOMB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3MQ3NOMBXVOFH2ZP2NQ3JVYXBE \
  | 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: db21b6b981bd5c53eb2fd361b4d7170906a3097620b8cc7d1d705f69a69475fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cf27d5ccefc203e5b1bc6e2d67d80a4018dabc1264a167a36cdbe03671b6763",
    "cross_cats_sorted": [
      "cs.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-01T04:25:00Z",
    "title_canon_sha256": "42b9a8ad6a05da7006e5e45c2beebc4a3a4008e900cd05de1d7ecab210201160"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00941",
    "kind": "arxiv",
    "version": 3
  }
}