Pith Number

pith:QASTZ5UY

pith:2026:QASTZ5UYRGLGABPMFC4LN53GUC

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SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants

Pietro Li\`o, Santanu Subhash Rathod, Xiao Zhang

SplineFlow uses B-spline interpolation to build stable conditional paths for flow matching in dynamical systems.

arxiv:2601.23072 v2 · 2026-01-30 · cs.LG

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Claims

C1strongest claim

We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met.

C2weakest assumption

That B-spline bases of appropriate order can capture higher-order dynamics from irregular observations without introducing instability or violating the required multi-marginal constraints, an assumption stated in the abstract but not derived in detail here.

C3one line summary

SplineFlow uses B-spline interpolation inside flow matching to jointly construct stable conditional paths that satisfy multi-marginal constraints for dynamical systems with irregular observations.

References

19 extracted · 19 resolved · 5 Pith anchors

[1] Building Normalizing Flows with Stochastic Interpolants · arXiv:2209.15571

[2] Random dynamical systems 1994

[3] Good approximation by splines with variable knots 1973

[4] A survey of the

[5] Flow matching meets biology and life science: A survey.arXiv preprint arXiv:2507.17731,

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:04.485178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80253cf69889966005ec28b8b6f766a0ba2e24ad0980eb42b8f32dc45533e1e6

Aliases

arxiv: 2601.23072 · arxiv_version: 2601.23072v2 · doi: 10.48550/arxiv.2601.23072 · pith_short_12: QASTZ5UYRGLG · pith_short_16: QASTZ5UYRGLGABPM · pith_short_8: QASTZ5UY

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/QASTZ5UYRGLGABPMFC4LN53GUC \
  | 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: 80253cf69889966005ec28b8b6f766a0ba2e24ad0980eb42b8f32dc45533e1e6

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-30T15:19:48Z",
    "title_canon_sha256": "a7695c957929ee02bc848a7ad4e12299bac5919c7761e4edfea2b6f392ed753a"
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