Traffic simulation is essential for validating the safety and reliability of autonomous driving systems, yet data-driven simulation methods often struggle with distribution shifts, limiting their generalizability across diverse datasets (domains). To address this, we present Causal Driving Pattern Transfer (CDPT), a novel two-stage knowledge distillation framework built upon diffusion model to enhance cross-domain generalizability. In Phase I, we implement hybrid self-distillation within the source domain by integrating feature-, response-, and contrastive-level distillation, which enables the model to decompose complex driving behaviors into their core causal components, including scene-conditioned driven patterns, multi-agent interaction dynamics and casual saliency. In Phase II, we introduce a continual distillation strategy: few-shot samples from the target domain are used to initiate generation of diverse synthetic scenarios, allowing the student model to continually adapt to novel environments without retraining on large-scale data. Extensive experiments demonstrates that CDPT achieves strong generalization in both open-loop and closed-loop simulations, effectively generating realistic, interaction-aware behaviors that are critical for scalable and reliable autonomous driving testing.