  Time Series Generation (TSG) has emerged as a pivotal technique in
synthesizing data that accurately mirrors real-world time series, becoming
indispensable in numerous applications. Despite significant advancements in
TSG, its efficacy frequently hinges on having large training datasets. This
dependency presents a substantial challenge in data-scarce scenarios,
especially when dealing with rare or unique conditions. To confront these
challenges, we explore a new problem of Controllable Time Series Generation
(CTSG), aiming to produce synthetic time series that can adapt to various
external conditions, thereby tackling the data scarcity issue.
  In this paper, we propose \textbf{C}ontrollable \textbf{T}ime \textbf{S}eries
(\textsf{CTS}), an innovative VAE-agnostic framework tailored for CTSG. A key
feature of \textsf{CTS} is that it decouples the mapping process from standard
VAE training, enabling precise learning of a complex interplay between latent
features and external conditions. Moreover, we develop a comprehensive
evaluation scheme for CTSG. Extensive experiments across three real-world time
series datasets showcase \textsf{CTS}'s exceptional capabilities in generating
high-quality, controllable outputs. This underscores its adeptness in
seamlessly integrating latent features with external conditions. Extending
\textsf{CTS} to the image domain highlights its remarkable potential for
explainability and further reinforces its versatility across different
modalities.
