Pith Number

pith:QVISCZET

pith:2026:QVISCZETLXX7NKDPOS6N532WAN

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Why DDIM Hallucinates More Than DDPM: A Theoretical Analysis of Reverse Dynamics

Abhinav N. Harish, Grigorios G. Chrysos, Hung Yun Tseng, Ishaan Kharbanda, Muhammad H. Ashiq, Samanyu Arora

DDIM reverse trajectories can trap on the line between two modes after a critical time, while DDPM noise lets them escape and reach the true modes.

arxiv:2605.06831 v2 · 2026-05-07 · cs.LG · cs.AI

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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 analyze the reverse ODE (DDIM) and SDE (DDPM) for a Gaussian mixture target, proving that after a critical time τ, (a) DDIM can become stuck on the segment connecting the two nearest modes and (b) DDPM *stochasticity* helps it become unstuck from this region, thus avoiding hallucination.

C2weakest assumption

The theoretical results and empirical observations are derived for a low-dimensional Gaussian mixture target; the same trapping behavior and benefit of stochasticity may not occur or may be harder to characterize for high-dimensional, non-Gaussian data distributions used in practice.

C3one line summary

DDIM gets stuck between modes in reverse diffusion on Gaussian mixtures after critical time τ, but DDPM stochasticity prevents this and lowers hallucination rates.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-01T01:02:41.899643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85512164935deff6a86f74bcdeef5603420cc74837beef9119d33065ed6598e6

Aliases

arxiv: 2605.06831 · arxiv_version: 2605.06831v2 · doi: 10.48550/arxiv.2605.06831 · pith_short_12: QVISCZETLXX7 · pith_short_16: QVISCZETLXX7NKDP · pith_short_8: QVISCZET

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QVISCZETLXX7NKDPOS6N532WAN \
  | 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: 85512164935deff6a86f74bcdeef5603420cc74837beef9119d33065ed6598e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba16023a18f482c3f4e89c9c73a902f8fcfe2dffd74f07a9403b1c06e1db13b3",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T18:34:12Z",
    "title_canon_sha256": "8b6ad8640fe227bb5b4ecb2c6c5e6519aaf86bf0bc307af4e6be6dce01563014"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06831",
    "kind": "arxiv",
    "version": 2
  }
}