Pith Number

pith:UI5O5LZY

pith:2026:UI5O5LZYHODE2GTPLL3MPA7JYO

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Coreset-Induced Conditional Velocity Flow Matching

Jianxi Su, Xiao Wang, Zihua She

A coreset-derived Gaussian mixture surrogate replaces isotropic noise in conditional velocity flow matching and equals the target-surrogate Wasserstein gap as transport cost.

arxiv:2605.12951 v1 · 2026-05-13 · stat.ML · cs.LG

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Claims

C1strongest claim

We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance.

C2weakest assumption

The explicit compression assumption that the coreset-derived Gaussian mixture surrogate sufficiently approximates the target velocity distribution so that the residual correction remains lightweight and the second-moment excess stays small.

C3one line summary

CCVFM replaces the inner noise source in hierarchical rectified flow matching with a data-informed Gaussian mixture surrogate from a Sinkhorn coreset, yielding a closed-form conditional velocity law and competitive few-step generation on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ.

References

33 extracted · 33 resolved · 2 Pith anchors

[1] Stochastic interpolants: A unifying framework for flows and diffusions.Journal of Machine Learning Research, 26(209):1–80, 2025 2025

[2] Reconstructing training data with informed adversaries 2022

[3] Pros and cons of GAN evaluation measures 2019

[4] Extracting training data from diffusion models 2023

[5] A downsampled variant of imagenet as an alternative to the CIFAR datasets 2017 · arXiv:1707.08819

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:09.405626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a23aeeaf383b864d1a6f5af6c783e9c39f826d5db7efcd3923355576dc0dce87

Aliases

arxiv: 2605.12951 · arxiv_version: 2605.12951v1 · doi: 10.48550/arxiv.2605.12951 · pith_short_12: UI5O5LZYHODE · pith_short_16: UI5O5LZYHODE2GTP · pith_short_8: UI5O5LZY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UI5O5LZYHODE2GTPLL3MPA7JYO \
  | 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: a23aeeaf383b864d1a6f5af6c783e9c39f826d5db7efcd3923355576dc0dce87

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "8152fabc43c0d8ac26acf4aff87461351dcb1a8e9f499cd08b7194e7fc1e6700",
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      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-13T03:34:40Z",
    "title_canon_sha256": "d2aaa81a9bcb98c658dcf83cbc55d11939f28260ca6c1d6e1581fd48a82a8fac"
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  "source": {
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