The rapid expansion of edge devices and Internet-of-Things (IoT) continues to heighten the demand for data transport under limited spectrum resources. The goal-oriented communications (GO-COM), unlike traditional communication systems designed for bit-level accuracy, prioritizes more critical information for specific application goals at the receiver. To improve the efficiency of generative learning models for GO-COM, this work introduces a novel noise-restricted diffusion-based GO-COM (Diff-GO$^\text{n}$) framework for reducing bandwidth overhead while preserving the media quality at the receiver. Specifically, we propose an innovative Noise-Restricted Forward Diffusion (NR-FD) framework to accelerate model training and reduce the computation burden for diffusion-based GO-COMs by leveraging a pre-sampled pseudo-random noise bank (NB). Moreover, we design an early stopping criterion for improving computational efficiency and convergence speed, allowing high-quality generation in fewer training steps. Our experimental results demonstrate superior perceptual quality of data transmission at a reduced bandwidth usage and lower computation, making Diff-GO$^\text{n}$ well-suited for real-time communications and downstream applications.