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

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/.