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/.

Modern generative models can create high-quality images and other data, but they are often slow because they require many iterative steps and rely on restrictive assumptions about the type of noise used in the generation process. Recent approaches improve flexibility but can make the generation process less stable and harder to control. In this work, we propose a new framework that balances flexibility and stability by learning how to efficiently transform a flexible generative process into a structured one that can be run in reverse. This allows us to generate samples in far fewer steps, including in a single step, while maintaining high quality. Our method can also recover standard diffusion models as a special case. Experiments across several generative tasks show that our approach is both effective and versatile. Code and demos are available at: https://oublalkhalid.github.io/MStar-Diffusion/.