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

arXiv: https://arxiv.org/abs/2605.06831 · HTML: https://mlsanity.com/paper/2605.06831/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 6 of 6)

- [Minimax Optimality of the Probability Flow ODE for Diffusion Models](https://mlsanity.com/paper/2503.09583/) (2025)
- [Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures](https://mlsanity.com/paper/2504.05300/) (2025)
- [Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance](https://mlsanity.com/paper/2508.03210/) (2025)
- [Counting Hallucinations in Diffusion Models](https://mlsanity.com/paper/2510.13080/) (2025)
- [Mitigating Diffusion Model Hallucinations with Dynamic Guidance](https://mlsanity.com/paper/2510.05356/) (2025)
- [Laplacian Score Sharpening for Mitigating Hallucination in Diffusion Models](https://mlsanity.com/paper/2511.07496/) (2025)

## Built on by (most cited first, 1 of 1)

- [Scaling and Distilling Text Embeddings for Better Diffusibility](https://mlsanity.com/paper/2610.01016/) (2026)

## Abstract (arXiv)

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 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. Our empirical validation verifies that DDPM has a significantly lower hallucination rate than DDIM when this region is entered. Building on our observations, we exhibit how using additional stochastic steps can help DDIM avoid hallucinations and offer new insights on how to design improved samplers.