Diffusion policies have recently emerged as a powerful paradigm for visuomotor control in robotic manipulation due to their ability to model the distribution of action sequences and capture multimodality. However, iterative denoising leads to substantial inference latency, limiting control frequency in real-time closed-loop systems. Existing acceleration methods either reduce sampling steps, bypass diffusion through direct prediction, or reuse past actions, but often struggle to jointly preserve action quality and achieve consistently low latency. In this work, we propose STEP, a lightweight spatiotemporal consistency prediction mechanism to construct high-quality warm-start actions that are both distributionally close to the target action and temporally consistent, without compromising the generative capability of the original diffusion policy. Then, we propose a velocity-aware perturbation injection mechanism that adaptively modulates actuation excitation based on temporal action variation to prevent execution stall especially for real-world tasks. We further provide a theoretical analysis showing that the proposed prediction induces a locally contractive mapping, ensuring convergence of action errors during diffusion refinement. We conduct extensive evaluations on nine simulated benchmarks and two real-world tasks. Notably, STEP with 2 steps can achieve an average 21.6% and 27.5% higher success rate than BRIDGER and DDIM on the RoboMimic benchmark and real-world tasks, respectively. These results demonstrate that STEP consistently advances the Pareto frontier of inference latency and success rate over existing methods.The code is publicly available at https://github.com/Kimho666/STEP.