Weather forecasts are inherently uncertain due to the chaotic nature of the atmosphere and unavoidable errors. Ensemble forecasting is the established approach for quantifying the uncertainty. However, it is both computationally expensive and inherently prone to under-dispersion, as it simulates multiple atmospheric trajectories with a finite number of members. In this study, we propose a novel paradigm that achieves uncertainty quantification by directly predicting forecast errors, thereby bypassing the need to simulate multiple trajectories. We employ a denoising diffusion probabilistic model for this task, as its generative capabilities are well-suited for learning high-dimensional distributions. By stochastically sampling from the learned distribution and adding the generated errors to the physics-based nowcast, an ensemble nowcast can be constructed efficiently without the need for perturbation generation or parallel model running. The proposed approach is applied to 10-meter wind speed nowcast, which is important but has received relatively limited attention in diffusion-based weather forecasting studies. Results show that the diffusion model effectively captures the spatial structure and probabilistic characteristics of forecast errors, leading to improved deterministic accuracy and a well-calibrated ensemble. In addition, different noise schedules for the diffusion process are systematically evaluated. The results indicate that the Cosine schedule provides the most reliable performance for uncertainty prediction, offering practical guidance for configuring diffusion models in weather forecasting applications.