Pith Number

pith:SRQXSWF6

pith:2026:SRQXSWF6VX2ACCUS64ZF2DZQBP

not attested not anchored not stored refs pending

Preconditioned Flow Matching

Eldad Haber, Eshed Gal, Md Shahriar Rahim Siddiqui, Moshe Eliasof, Shadab Ahamed, Simon Ghyselincks

Preconditioning transforms targets to isotropic space to reshape flow matching paths and fix ill-conditioned optimization.

arxiv:2603.02337 v2 · 2026-03-02 · cs.LG · cs.AI · cs.CV

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

We propose preconditioned flow matching, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning.

C2weakest assumption

The assumption that an effective preconditioner exists which can be applied without introducing new optimization difficulties or distorting the probability paths in a way that invalidates the flow matching objective.

C3one line summary

Preconditioned flow matching transforms target distributions to isotropic representations to fix ill-conditioned optimization in standard flow matching.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

RiT: Vanilla Diffusion Transformers Suffice in Representation Space

Receipt and verification

First computed	2026-05-18T03:09:23.166936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94617958beadf4010a92f7325d0f300be322ebd7e4bd33b1db94139de227c6e5

Aliases

arxiv: 2603.02337 · arxiv_version: 2603.02337v2 · doi: 10.48550/arxiv.2603.02337 · pith_short_12: SRQXSWF6VX2A · pith_short_16: SRQXSWF6VX2ACCUS · pith_short_8: SRQXSWF6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SRQXSWF6VX2ACCUS64ZF2DZQBP \
  | 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: 94617958beadf4010a92f7325d0f300be322ebd7e4bd33b1db94139de227c6e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f82d9cbde890954c96bb660ae47ae3beffc3e8acf2003284ad1a1f3f4f704c72",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-02T19:09:15Z",
    "title_canon_sha256": "e4433be4b722edab0843c62d68496fafab0d6be6ca150dacc1a83daa51daba46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.02337",
    "kind": "arxiv",
    "version": 2
  }
}