Autoregressive Denoising Diffusion Models for Multivariate Probabilistic\n Time Series Forecasting

In this work, we propose \\texttt{TimeGrad}, an autoregressive model for\nmultivariate probabilistic time series forecasting which samples from the data\ndistribution at each time step by estimating its gradient. To this end, we use\ndiffusion probabilistic models, a class of latent variable models closely\nconnected to score matching and energy-based methods. Our model learns\ngradients by optimizing a variational bound on the data likelihood and at\ninference time converts white noise into a sample of the distribution of\ninterest through a Markov chain using Langevin sampling. We demonstrate\nexperimentally that the proposed autoregressive denoising diffusion model is\nthe new state-of-the-art multivariate probabilistic forecasting method on\nreal-world data sets with thousands of correlated dimensions. We hope that this\nmethod is a useful tool for practitioners and lays the foundation for future\nresearch in this area.\n