Partially Functional Dynamic Backdoor Diffusion-based Causal Model

Causal inference in settings involving complex spatio-temporal dependencies, such as environmental epidemiology, is challenging due to the presence of unmeasured confounding. However, a significant gap persists in existing methods: current diffusion-based causal models rely on restrictive assumptions of causal sufficiency or static confounding. To address this limitation, we introduce the Partially Functional Dynamic Backdoor Diffusion-based Causal Model (PFD-BDCM), a generative framework designed to bridge this gap. Our approach uniquely incorporates valid backdoor adjustments into the diffusion sampling mechanism to mitigate bias from unmeasured confounders. Specifically, it captures their intricate dynamics through region-specific structural equations and conditional autoregressive processes, and accommodates multi-resolution variables via functional data techniques. Furthermore, we provide theoretical guarantees by establishing error bounds for counterfactual estimates. Extensive experiments on synthetic data and a real-world air pollution case study confirm that PFD-BDCM outperforms current state-of-the-art methods.