Title: Modeling Temporal Data as Continuous Functions with Process Diffusion. Abstract: Temporal data like time series are often observed at irregular intervals which is a challenging setting for  the existing machine learning methods. To tackle this problem, we view such data as samples from some underlying continuous function. We then define a diffusion-based generative model that adds  noise from a predefined stochastic process while  preserving the  continuity of the resulting underlying function. A neural network is trained to reverse this process which allows us to sample new realizations from the learned distribution. We define suitable stochastic processes as noise sources and introduce novel denoising and score-matching models on processes. Further, we show how to apply this approach to the  multivariate probabilistic forecasting and imputation tasks. Through our extensive experiments, we demonstrate that our method outperforms previous models on synthetic and real-world datasets.