Causal time series generation via diffusion models

Time series generation (TSG) synthesizes realistic sequences and has achieved remarkable success. Among TSG, conditional models generate sequences given observed covariates, however, such models learn observational correlations without considering unobserved confounding. In this work, we propose a causal perspective on conditional TSG and introduce causal time series generation as a new TSG task family, formalized within Pearl’s causal ladder, extending beyond observational generation to include interventional and counterfactual settings. To instantiate these tasks, we develop CaTSG, a unified diffusion-based framework whose sampling is guided by backdoor-adjusted score functions targeting interventional and counterfactual distributions under an assumed SCM, while preserving observational fidelity. Extensive experiments on synthetic and real-world datasets show that CaTSG achieves superior fidelity, and on a known-SCM synthetic system, where the interventional target can be constructed directly, it attains the best score on every evaluated metric under multiple environment marginals. Overall, we formalize the causal TSG family and present CaTSG as a first instantiation, providing empirical evidence on synthetic and real-world settings and opening a direction for interventional and counterfactual generation.