{"paper":{"title":"Why DDIM Hallucinates More Than DDPM: A Theoretical Analysis of Reverse Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"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.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Abhinav N. Harish, Grigorios G. Chrysos, Hung Yun Tseng, Ishaan Kharbanda, Muhammad H. Ashiq, Samanyu Arora","submitted_at":"2026-05-07T18:34:12Z","abstract_excerpt":"We theoretically study the hallucination phenomena in two canonical diffusion samplers: the stochastic Denoising Diffusion Probabilistic Model (DDPM) and the deterministic Denoising Diffusion Implicit Model (DDIM). We analyze the reverse ODE (DDIM) and SDE (DDPM) for a Gaussian mixture target, proving that after a critical time $\\tau$, (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. Our empirical validation verifies that DDPM has a significantly lower hallucination rate"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"DDIM gets stuck between modes in reverse diffusion on Gaussian mixtures after critical time τ, but DDPM stochasticity prevents this and lowers hallucination rates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5ae3a7f4ea2d47321148418e583b19531664d21c8ead6de4fa64486b0c427905"},"source":{"id":"2605.06831","kind":"arxiv","version":2},"verdict":{"id":"5bca75f3-6297-4762-b033-2977adb5dc27","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T00:55:51.480715Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06831/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:02:03.778189Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T07:34:09.925892Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:18.715433Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:22:34.822230Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0e3735f6ae796db1a6957894555c367fc64a16be58a0e7b62c181d3d345a0023"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ba5d9505a2e2deb383cf8e71eae5fca22c28c51f84e4e3254d9ad4f2de41b206"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}