Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

翻译：时间序列等时域数据可视为对潜在函数的离散化观测。为构建此类数据的生成模型，需对支配其的随机过程进行建模。本文通过定义函数空间中的去噪扩散模型，提出一种能够自然处理非均匀采样观测的解决方案。前向过程逐步向函数添加噪声以保持其连续性，而学习得到的反向过程则消除噪声并生成新样本作为函数输出。为此，我们定义了合适的噪声源，并引入新型去噪与得分匹配模型。实验表明，本方法可用于多元概率预测与插值任务，且该模型可被解释为一种神经过程。