Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $θ\in \mathbb{R}^d$. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of $n$ and $θ$, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.

It is currently difficult to distill discrete diffusion models. In contrast, continuous diffusion literature has many distillation approaches methods that can reduce sampling steps to a handful. Our method, Discrete Moment Matching Distillation (D-MMD), leverages ideas that have been highly successful in the continuous domain. Whereas previous discrete distillation methods collapse, D-MMD maintains high quality and diversity (given sufficient sampling steps). This is demonstrated on both text and image datasets. Moreover, the newly distilled generators can outperform their teachers.

Sudan's army has denied it carried out a deadly attack on a major hospital on Friday night in a city in the west of the country held by its rivals, the paramilitary Rapid Support Forces (RSF). The head of the World Health Organization (WHO) said 64 people - including 13 children, two nurses and a doctor - had died in the strike on el-Daein Teaching Hospital and 89 others had been wounded. Enough blood has been spilled, Tedros Adhanom Ghebreyesus posted on X, urging the warring parties to end the conflict, which started nearly three years ago. The RSF said an army drone had hit the hospital in el-Daein, the capital of East Darfur state, on the day Muslims were marking the festival of Eid. Sudan was plunged into a civil war in April 2023 when a vicious struggle for power broke out between the military and the RSF, who had once been allies after coming to power in a coup in 2021.

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