Pith Number

pith:6W6U7QBC

pith:2026:6W6U7QBC6QY7IXTXYH7UIPB5BS

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Rethinking Forward Processes for Score-Based Nonlinear Data Assimilation in High Dimensions

Dae Wook Kim, Donghan Kim, Eunbi Yoon, Won Chang

A measurement-aware forward process built from the measurement equation yields exact likelihood scores for score-based data assimilation.

arxiv:2604.02889 v2 · 2026-04-03 · stat.ML · cs.AI · cs.LG

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\pithnumber{6W6U7QBC6QY7IXTXYH7UIPB5BS}

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Claims

C1strongest claim

we propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation. This construction makes the likelihood score analytically tractable: for linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score.

C2weakest assumption

That constructing the forward process directly from the measurement equation preserves the diffusion properties needed for stable score-based sampling and does not introduce new instabilities or approximation errors in high dimensions.

C3one line summary

A measurement-aware forward process for score-based data assimilation yields an exact likelihood score for linear measurements by construction.

Receipt and verification

First computed	2026-05-22T01:04:01.398360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5bd4fc022f431f45e77c1ff443c3d0c911db5a729c9b42b5e812db7b34d4c6d

Aliases

arxiv: 2604.02889 · arxiv_version: 2604.02889v2 · doi: 10.48550/arxiv.2604.02889 · pith_short_12: 6W6U7QBC6QY7 · pith_short_16: 6W6U7QBC6QY7IXTX · pith_short_8: 6W6U7QBC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6W6U7QBC6QY7IXTXYH7UIPB5BS \
  | 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: f5bd4fc022f431f45e77c1ff443c3d0c911db5a729c9b42b5e812db7b34d4c6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "408ef432600de3bc4a761d9efb6c6287741e3bde2bbc3206d39bba47f1b67787",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-04-03T08:55:38Z",
    "title_canon_sha256": "0827e06615fc21b109a7f8f879f5d82affdd0c0668098fbe2e642a0397705c94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.02889",
    "kind": "arxiv",
    "version": 2
  }
}