Pith Number

pith:462JYRJZ

pith:2026:462JYRJZ3MVIEPD6HE5Y7N6T5F

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Path-independent Flow Matching for Multi-parameter Generative Dynamics

AmirHossein Zamani, Eugene Belilovsky, Francisco T\'ellez, Guy Wolf, Philippe Martin, Shuang Ni, Sina Sanjari, Yanlei Zhang

Path-independent Flow Matching learns vector fields whose flows produce transport that depends only on start and end distributions, not the path taken.

arxiv:2605.13487 v1 · 2026-05-13 · cs.LG

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Claims

C1strongest claim

we introduce Path-independent Flow Matching (PiFM), a method for learning vector fields whose induced flows yield path-independent transport between distributions. We show that, under suitable assumptions, PiFM approximates the Wasserstein barycenter

C2weakest assumption

under suitable assumptions, PiFM approximates the Wasserstein barycenter; the structural conditions that enforce path-independence in higher-dimensional parameter domains are not specified in the abstract.

C3one line summary

PiFM extends Flow Matching to multi-parameter settings by enforcing path-independent flows that approximate Wasserstein barycenters under suitable assumptions.

References

46 extracted · 46 resolved · 0 Pith anchors

[1] Multi-marginal optimal transport: theory and applications 2015 · doi:10.1051/m2an/2015020

[2] Unbalanced Multi-marginal Optimal Transport , volume= · doi:10.1007/s10851-022-01126-7

[3] Characterization of barycenters in the Wasserstein space by averaging optimal transport maps , author=. 2017 , eprint= 2017

[4] Marsden and Tudor Ratiu , title = 1984

[5] Foundations of Differentiable Manifolds and Lie Groups , author=. 1983 , publisher= 1983

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:41.245186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7b49c4539db2a823c7e393b8fb7d3e966d524ce0122b16eda4acaf5a28a59a5

Aliases

arxiv: 2605.13487 · arxiv_version: 2605.13487v1 · doi: 10.48550/arxiv.2605.13487 · pith_short_12: 462JYRJZ3MVI · pith_short_16: 462JYRJZ3MVIEPD6 · pith_short_8: 462JYRJZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/462JYRJZ3MVIEPD6HE5Y7N6T5F \
  | 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: e7b49c4539db2a823c7e393b8fb7d3e966d524ce0122b16eda4acaf5a28a59a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14d226fe7ff824794f333bd258125329a947a3199c74813e766551abef84ca65",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T13:12:50Z",
    "title_canon_sha256": "1c2c263ee2c20edae62fb725bcefc464fa9bd4dfe2e13618b7ff1e62484c022a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13487",
    "kind": "arxiv",
    "version": 1
  }
}