Pith Number

pith:2XM5CQTV

pith:2026:2XM5CQTV2CAP65WI4OHY4IRXYJ

not attested not anchored not stored refs resolved

The critical slowing down in diffusion models

Giulio Biroli, Luca Maria Del Bono, Marylou Gabri\'e, Patrick Charbonneau

Two-layer networks with local score approximation reduce critical slowing down in diffusion models to logarithmic scaling.

arxiv:2605.12597 v1 · 2026-05-12 · cond-mat.dis-nn · cond-mat.stat-mech · cs.AI · cs.LG · physics.comp-ph

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Using a two-layer architecture drastically reduces the critical slowing down, with the training time scaling logarithmically rather than quadratically with system size. By introducing a local score approximation we show that this acceleration in training time can be achieved without increasing the number of neural network parameters.

C2weakest assumption

That the Gaussian limit n→∞ of the O(n) model and the one-layer network exactly matching its score function are representative of the critical slowing down that occurs in practical diffusion models trained on finite-n or non-Gaussian systems.

C3one line summary

Diffusion models on the Gaussian O(n) model exhibit critical slowing down with shallow networks that deeper local score approximations can reduce to logarithmic training-time scaling.

References

103 extracted · 103 resolved · 1 Pith anchors

[1] (14) with the Fourier space kernel in Eq

[2] (22)—the generation dynamics Eq

[3] MUR PON Ricerca e Innovazione 2014-2020 2014

[4] G.Battimelli, G.Ciccotti, P.Greco,andG.Giobbi,Com- puter Meets Theoretical Physics: The New Frontier of Molecular Simulation(Springer, 2020) 2020

[5] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimiza- tion by simulated annealing, Science220, 671 (1983) 1983

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:01.171182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5d9d14275d080ff76c8e38f8e2237c27f0c457d3f01ecc9ef4dd40fd8a0fa81

Aliases

arxiv: 2605.12597 · arxiv_version: 2605.12597v1 · doi: 10.48550/arxiv.2605.12597 · pith_short_12: 2XM5CQTV2CAP · pith_short_16: 2XM5CQTV2CAP65WI · pith_short_8: 2XM5CQTV

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/2XM5CQTV2CAP65WI4OHY4IRXYJ \
  | 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: d5d9d14275d080ff76c8e38f8e2237c27f0c457d3f01ecc9ef4dd40fd8a0fa81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "766a3a8d5c285da4726732de0461164764b193fed63f032abd94d4a013a77bac",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.AI",
      "cs.LG",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-05-12T18:00:02Z",
    "title_canon_sha256": "c0f6406917aebddba081a0761924fa17c9f4e9bd5c12bffc813f279c6bb2b535"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12597",
    "kind": "arxiv",
    "version": 1
  }
}