Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To do so, we represent functional data in spectral space to dissociate the stochastic part of the processes from their space-time part. Using dimensionality reduction techniques we then sample from their stochastic component using finite dimensional SGM. We demonstrate our method's effectiveness for modelling various multimodal datasets.
翻译:基于分数的基因模型(SGM)已证明是模拟有限维空间密度的一个非常有效的方法。 在这项工作中,我们提议扩大这一方法,以在功能空间学习基因模型。为了这样做,我们代表光谱空间的功能性数据,将过程的随机部分与其空间时段分离。我们利用维度减少技术,然后利用有限的维度SGM从它们随机组件中取样。我们展示了我们模拟各种多式数据集的方法的有效性。