M-Star: Markovian Projection of Star-Shaped Diffusion for Exponential Family Distributions

François Bertholom, Khalid Oublal
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:7791-7814, 2026.

Abstract

Diffusion models achieve state-of-the-art performance in generative modeling but are limited by their reliance on Gaussian noise and the high computational cost of iterative sampling. Star-shaped diffusion addresses the former by introducing a non-Markovian forward process, yet this comes at the expense of temporal coherence in the reverse process. We propose a novel framework that resolves this trade-off by learning a Markovian projection of a star-shaped forward process, and its reversal. This design enables learning over a broad class of exponential models and recovers DDPM as a special case. It is particularly well-suited for knowledge distillation, allowing few-step or even single-step generation. Experiments demonstrate the effectiveness and flexibility of our approach across multiple generative tasks. Code and demo are available at: https://oublalkhalid.github.io/MStar-Diffusion/.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-bertholom26a, title = {M-Star: {M}arkovian Projection of Star-Shaped Diffusion for Exponential Family Distributions}, author = {Bertholom, Fran\c{c}ois and Oublal, Khalid}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {7791--7814}, 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/bertholom26a/bertholom26a.pdf}, url = {https://proceedings.mlr.press/v306/bertholom26a.html}, abstract = {Diffusion models achieve state-of-the-art performance in generative modeling but are limited by their reliance on Gaussian noise and the high computational cost of iterative sampling. Star-shaped diffusion addresses the former by introducing a non-Markovian forward process, yet this comes at the expense of temporal coherence in the reverse process. We propose a novel framework that resolves this trade-off by learning a Markovian projection of a star-shaped forward process, and its reversal. This design enables learning over a broad class of exponential models and recovers DDPM as a special case. It is particularly well-suited for knowledge distillation, allowing few-step or even single-step generation. Experiments demonstrate the effectiveness and flexibility of our approach across multiple generative tasks. Code and demo are available at: https://oublalkhalid.github.io/MStar-Diffusion/.} }
Endnote
%0 Conference Paper %T M-Star: Markovian Projection of Star-Shaped Diffusion for Exponential Family Distributions %A François Bertholom %A Khalid Oublal %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-bertholom26a %I PMLR %P 7791--7814 %U https://proceedings.mlr.press/v306/bertholom26a.html %V 306 %X Diffusion models achieve state-of-the-art performance in generative modeling but are limited by their reliance on Gaussian noise and the high computational cost of iterative sampling. Star-shaped diffusion addresses the former by introducing a non-Markovian forward process, yet this comes at the expense of temporal coherence in the reverse process. We propose a novel framework that resolves this trade-off by learning a Markovian projection of a star-shaped forward process, and its reversal. This design enables learning over a broad class of exponential models and recovers DDPM as a special case. It is particularly well-suited for knowledge distillation, allowing few-step or even single-step generation. Experiments demonstrate the effectiveness and flexibility of our approach across multiple generative tasks. Code and demo are available at: https://oublalkhalid.github.io/MStar-Diffusion/.
APA
Bertholom, F. & Oublal, K.. (2026). M-Star: Markovian Projection of Star-Shaped Diffusion for Exponential Family Distributions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:7791-7814 Available from https://proceedings.mlr.press/v306/bertholom26a.html.

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