Why DDIM Hallucinates More than DDPM: A Theoretical Analysis of Reverse Dynamics
Provides theoretical understanding of hallucination in diffusion samplers for generative modeling practitioners.
The paper theoretically analyzes why DDIM hallucinates more than DDPM in diffusion models, proving that DDPM's stochasticity helps it avoid getting stuck between modes, and shows that adding stochastic steps to DDIM reduces hallucination.
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.