Language-driven grasp detection is a fundamental yet challenging task in robotics with various industrial applications. In this work, we present a new approach for language-driven grasp detection that leverages the concept of lightweight diffusion models to achieve fast inference time. By integrating diffusion processes with grasping prompts in natural language, our method can effectively encode visual and textual information, enabling more accurate and versatile grasp positioning that aligns well with the text query. To overcome the long inference time problem in diffusion models, we leverage the image and text features as the condition in the consistency model to reduce the number of denoising timesteps during inference. The intensive experimental results show that our method outperforms other recent grasp detection methods and lightweight diffusion models by a clear margin. We further validate our method in real-world robotic experiments to demonstrate its fast inference time capability.