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

Muhammad H. Ashiq, Samanyu Arora, Abhinav Narayan Harish, Ishaan Kharbanda, Hung Yun Tseng, Grigorios Chrysos
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:4105-4157, 2026.

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 $\tau$, (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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ashiq26a, title = {Why {DDIM} Hallucinates More Than {DDPM}: A Theoretical Analysis of Reverse Dynamics}, author = {Ashiq, Muhammad H. and Arora, Samanyu and Harish, Abhinav Narayan and Kharbanda, Ishaan and Tseng, Hung Yun and Chrysos, Grigorios}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {4105--4157}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ashiq26a/ashiq26a.pdf}, url = {https://proceedings.mlr.press/v306/ashiq26a.html}, 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 $\tau$, (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 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.} }
Endnote
%0 Conference Paper %T Why DDIM Hallucinates More Than DDPM: A Theoretical Analysis of Reverse Dynamics %A Muhammad H. Ashiq %A Samanyu Arora %A Abhinav Narayan Harish %A Ishaan Kharbanda %A Hung Yun Tseng %A Grigorios Chrysos %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ashiq26a %I PMLR %P 4105--4157 %U https://proceedings.mlr.press/v306/ashiq26a.html %V 306 %X 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 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.
APA
Ashiq, M.H., Arora, S., Harish, A.N., Kharbanda, I., Tseng, H.Y. & Chrysos, G.. (2026). Why DDIM Hallucinates More Than DDPM: A Theoretical Analysis of Reverse Dynamics. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:4105-4157 Available from https://proceedings.mlr.press/v306/ashiq26a.html.

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