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

2026-05-07

AI Summary

This work investigates the fundamental reason why Denoising Diffusion Implicit Models (DDIM) are more prone to hallucination—i.e., generating out-of-distribution samples—compared to Denoising Diffusion Probabilistic Models (DDPM). By theoretically analyzing the deterministic ordinary differential equation (ODE) of DDIM and the stochastic differential equation (SDE) reverse dynamics of DDPM under a Gaussian mixture target distribution, the study establishes that DDIM trajectories tend to become trapped along line segments between modes after a critical time, whereas the inherent stochasticity in DDPM enables escape from such regions, thereby suppressing hallucinations. Building on this insight, the authors propose a novel strategy that introduces stochastic steps into the DDIM sampling process. Numerical experiments confirm that DDPM exhibits significantly lower hallucination rates in mode-connecting regions and demonstrate that the proposed method effectively mitigates hallucination in DDIM.

Abstract

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.

Problem

• hallucination
• DDIM
• DDPM
• diffusion models
• reverse dynamics

Innovation

• diffusion models
• hallucination
• DDIM
• DDPM
• stochasticity