Pith Number

pith:6J435JFE

pith:2025:6J435JFEV4NLMP43G5M6KCYQVZ

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On The Hidden Biases of Flow Matching Samplers

Soon Hoe Lim

Replacing the target distribution with finite-sample surrogates in flow matching introduces three coupled biases that alter learned paths and dynamics.

arxiv:2512.16768 v3 · 2025-12-18 · stat.ML · cs.LG · math.PR

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Claims

C1strongest claim

For affine conditional flows, the exact empirical minimizer is derived and a smoothed plug-in regime yields a terminal law that is exactly a kernel-mixture estimator; fixed empirical marginal paths admit explicit flux-null corrections to the dynamics.

C2weakest assumption

The derivations rely on the assumption that conditional flows are affine and that the plug-in hierarchy (empirical measure to smoothed estimators) is the appropriate finite-sample surrogate for the target distribution.

C3one line summary

Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.

References

51 extracted · 51 resolved · 7 Pith anchors

[1] Stochastic Interpolants: A Unifying Framework for Flows and Diffusions 2023 · arXiv:2303.08797

[2] Learning to sample better.Journal of Sta- tistical Mechanics: Theory and Experiment, 2024(10):104014, 2024 2024

[3] Luigi Ambrosio, Nicola Gigli, and Giuseppe Savar´ e.Gradient Flows: In Metric Spaces And In the Space of Probability Measures. Springer, 2005 2005

[4] Bronstein, Pierre Vandergheynst, and Adam Gosztolai 2025

[5] Memorization and regularization in generative diffusion models.arXiv preprint arXiv:2501.15785 2025

Formal links

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Cited by

1 paper in Pith

Is Flow Matching Just Trajectory Replay for Sequential Data?

Receipt and verification

First computed	2026-05-17T23:39:00.456667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f279bea4a4af1ab63f9b3759e50b10ae6a6d391e17a31605acbd355285c6e9c8

Aliases

arxiv: 2512.16768 · arxiv_version: 2512.16768v3 · doi: 10.48550/arxiv.2512.16768 · pith_short_12: 6J435JFEV4NL · pith_short_16: 6J435JFEV4NLMP43 · pith_short_8: 6J435JFE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6J435JFEV4NLMP43G5M6KCYQVZ \
  | 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: f279bea4a4af1ab63f9b3759e50b10ae6a6d391e17a31605acbd355285c6e9c8

Canonical record JSON

{
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    "abstract_canon_sha256": "1777a5b347d51d56be82ab65fde97044914f89ddff14aa6beb10ae9db2452f22",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-12-18T17:02:11Z",
    "title_canon_sha256": "d2c2ac94d61b772aa6089a2667560162c8035f6767c8f86976629e208297ca01"
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  "source": {
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    "kind": "arxiv",
    "version": 3
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}