  Synthetic time series are often used in practical applications to augment the
historical time series dataset for better performance of machine learning
algorithms, amplify the occurrence of rare events, and also create
counterfactual scenarios described by the time series.
Distributional-similarity (which we refer to as realism) as well as the
satisfaction of certain numerical constraints are common requirements in
counterfactual time series scenario generation requests. For instance, the US
Federal Reserve publishes synthetic market stress scenarios given by the
constrained time series for financial institutions to assess their performance
in hypothetical recessions. Existing approaches for generating constrained time
series usually penalize training loss to enforce constraints, and reject
non-conforming samples. However, these approaches would require re-training if
we change constraints, and rejection sampling can be computationally expensive,
or impractical for complex constraints. In this paper, we propose a novel set
of methods to tackle the constrained time series generation problem and provide
efficient sampling while ensuring the realism of generated time series. In
particular, we frame the problem using a constrained optimization framework and
then we propose a set of generative methods including "GuidedDiffTime", a
guided diffusion model to generate realistic time series. Empirically, we
evaluate our work on several datasets for financial and energy data, where
incorporating constraints is critical. We show that our approaches outperform
existing work both qualitatively and quantitatively. Most importantly, we show
that our "GuidedDiffTime" model is the only solution where re-training is not
necessary for new constraints, resulting in a significant carbon footprint
reduction, up to 92% w.r.t. existing deep learning methods.
