  Diffusion models have achieved state-of-the-art performance in generative
modeling tasks across various domains. Prior works on time series diffusion
models have primarily focused on developing conditional models tailored to
specific forecasting or imputation tasks. In this work, we explore the
potential of task-agnostic, unconditional diffusion models for several time
series applications. We propose TSDiff, an unconditionally-trained diffusion
model for time series. Our proposed self-guidance mechanism enables
conditioning TSDiff for downstream tasks during inference, without requiring
auxiliary networks or altering the training procedure. We demonstrate the
effectiveness of our method on three different time series tasks: forecasting,
refinement, and synthetic data generation. First, we show that TSDiff is
competitive with several task-specific conditional forecasting methods
(predict). Second, we leverage the learned implicit probability density of
TSDiff to iteratively refine the predictions of base forecasters with reduced
computational overhead over reverse diffusion (refine). Notably, the generative
performance of the model remains intact -- downstream forecasters trained on
synthetic samples from TSDiff outperform forecasters that are trained on
samples from other state-of-the-art generative time series models, occasionally
even outperforming models trained on real data (synthesize).
