Latent Causal Flow: Continuous Backdoor Adjustment for Time Series Generation

Deep generative models have achieved remarkable success in time series generation, yet they largely neglect interventional and counterfactual inference. Existing causal generative methods typically rely on discrete environment prototypes, which fail to capture the continuous nature of real-world confounding. To address this, we propose Latent Causal Flow (LCF), a flow matching framework that models latent confounders as a continuous space with an Unconditional Latent Environment Prior, enabling smooth interpolation and fine-grained control over confounding effects. We provide theoretical justification by proving that Pearl's backdoor adjustment corresponds to the expectation of velocity fields over a continuous latent distribution. Furthermore, we propose an environment-aware velocity architecture that integrates dual-path environment injection, along with a Causal Pathway Disentanglement mechanism, enabling effective utilization of latent environments and explicit disentanglement of condition-driven, environment-driven, and interaction-driven causal effects. Experiments on synthetic and real-world datasets demonstrate that LCF achieves state-of-the-art performance while providing reliable causal inference capabilities. Code is available at https://github.com/decisionintelligence/LCF.