  The imputation of missing values represents a significant obstacle for many
real-world data analysis pipelines. Here, we focus on time series data and put
forward SSSD, an imputation model that relies on two emerging technologies,
(conditional) diffusion models as state-of-the-art generative models and
structured state space models as internal model architecture, which are
particularly suited to capture long-term dependencies in time series data. We
demonstrate that SSSD matches or even exceeds state-of-the-art probabilistic
imputation and forecasting performance on a broad range of data sets and
different missingness scenarios, including the challenging blackout-missing
scenarios, where prior approaches failed to provide meaningful results.
