Diffusion-based models have shown strong performance in video super-resolution (VSR) and video frame interpolation (VFI). However, their role in the coupled space-time video super-resolution (STVSR) setting remains limited. Existing diffusion-based STVSR approaches suffer from two issues: (1) low inference efficiency and (2) insufficient utilization of spatiotemporal information. These limitations impede deployment. To address these issues, we introduce DiffST, an efficient spatiotemporal-aware video diffusion framework for real-world STVSR. To improve efficiency, we adapt a pre-trained diffusion model for one-step sampling and process the entire video directly rather than operating on individual frames. Furthermore, to enhance spatiotemporal information utilization, we introduce cross-frame context aggregation (CFCA) and video representation guidance (VRG). The CFCA module aggregates information across multiple keyframes to produce intermediate frames. The VRG module extracts video-level global features to guide the diffusion process. Extensive experiments show that DiffST obtains leading results on real-world STVSR tasks. It also maintains high inference efficiency, running about 17$\times$ faster than previous diffusion-based STVSR methods. Code is available at: https://github.com/zhengchen1999/DiffST.