Speech enhancement (SE) is the fundamental task of enhancing the clarity and quality of speech in the presence of non-stationary additive noise. While deterministic deep learning models have been commonly employed for SE, recent research indicates that generative models, such as denoising diffusion probabilistic models (DDPMs), have shown promise. However, different from speech generation, SE has a strong constraint to generate results in accordance with the underlying ground-truth signal. Additionally, for a wide variety of applications, SE systems need to be employed in real-time, and traditional diffusion models (DMs) requiring many iterations of a large model during inference are inefficient. To address these issues, we propose ProSE (diffusion-based Priors for SE), a novel methodology based on an alternative framework for applying diffusion models to SE. Specifically, we first apply DDPMs to generate priors in a latent space due to their powerful distribution mapping capabilities. The priors are then integrated into a transformer-based regression model for SE. The priors guide the regression model in the enhancement process. Since the diffusion process is applied to a compact latent space, the diffusion model takes fewer iterations than the traditional DM to obtain accurate estimations. Additionally, using a regression model for SE avoids the distortion issue caused by misaligned details generated by DMs. Comprehensive experiments show that ProSE achieves state-of-the-art performance on synthetic and real-world datasets using various metrics while consuming less computational costs.