Current generative models struggle to synthesize dynamic 4D driving scenes that simultaneously support temporal extrapolation and spatial novel view synthesis (NVS) without per-scene optimization. A key challenge lies in finding an efficient and generalizable geometric representation that seamlessly connects temporal and spatial synthesis. To address this, we propose DiST-4D, the first disentangled spatiotemporal diffusion framework for 4D driving scene generation, which leverages metric depth as the core geometric representation. DiST-4D decomposes the problem into two diffusion processes: DiST-T, which predicts future metric depth and multi-view RGB sequences directly from past observations, and DiST-S, which enables spatial NVS by training only on existing viewpoints while enforcing cycle consistency. This cycle consistency mechanism introduces a forward-backward rendering constraint, reducing the generalization gap between observed and unseen viewpoints. Metric depth is essential for both accurate reliable forecasting and accurate spatial NVS, as it provides a view-consistent geometric representation that generalizes well to unseen perspectives. Experiments demonstrate that DiST-4D achieves state-of-the-art performance in both temporal prediction and NVS tasks, while also delivering competitive performance in planning-related evaluations.