Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalising this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications.

翻译：去噪扩散是当前性能最优异的生成模型之一，展现出卓越的实证表现。其原理是将数据分布扩散为高斯分布，然后学习逆转这一加噪过程以生成合成数据点。该模型通过评分匹配技术近似含噪数据密度的对数导数来实现去噪。当仅能从前验分布和似然函数进行采样时，此类模型同样适用于执行近似后验模拟。我们提出一个统一框架，将该方法推广至更广泛的空间类别，并由此衍生出评分匹配的创新扩展。最终通过多类应用实例验证了所提模型的效用。