Pith Number

pith:BPZB3OHI

pith:2026:BPZB3OHIKGIYXMJGHX7QFBAFMV

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Improving Classifier-Free Guidance of Flow Matching via Manifold Projection

Chao Wang, Haixia Liu, Jian-Feng Cai, Zhengyi Su

Reformulating classifier-free guidance in flow matching as manifold-constrained homotopy optimization reduces sensitivity to guidance scales.

arxiv:2601.21892 v2 · 2026-01-29 · cs.CV · cs.AI

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\usepackage{pith}
\pithnumber{BPZB3OHIKGIYXMJGHX7QFBAFMV}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We reformulate the CFG sampling as a homotopy optimization with a manifold constraint. This formulation necessitates a manifold projection step, which we implement via an incremental gradient descent scheme during sampling.

C2weakest assumption

That the velocity field in flow matching exactly corresponds to the gradient of a sequence of smoothed distance functions guiding latent variables toward the scaled target image set, making standard CFG merely an approximation whose gap controls sensitivity.

C3one line summary

Reformulates CFG sampling in flow matching as homotopy optimization with manifold projection via incremental gradient descent and Anderson acceleration, yielding better fidelity and robustness without retraining.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:24.099324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bf21db8e851918bb1263dff0284056554661e20552fa154f622207d8516802a

Aliases

arxiv: 2601.21892 · arxiv_version: 2601.21892v2 · doi: 10.48550/arxiv.2601.21892 · pith_short_12: BPZB3OHIKGIY · pith_short_16: BPZB3OHIKGIYXMJG · pith_short_8: BPZB3OHI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BPZB3OHIKGIYXMJGHX7QFBAFMV \
  | 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: 0bf21db8e851918bb1263dff0284056554661e20552fa154f622207d8516802a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dbdb68d2c990ee0c961abb609095cfbceee3d44e1890a34583508fb81552a57",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-01-29T15:49:31Z",
    "title_canon_sha256": "c45fbbc391060580efa72447877bc0a05d7db1f3dd9dfd57f8b10877e43ac96c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.21892",
    "kind": "arxiv",
    "version": 2
  }
}