Extensive pre-training with large data is indispensable for downstream geometry and semantic visual perception tasks. Thanks to large-scale text-to-image (T2I) pretraining, recent works show promising results by simply fine-tuning T2I diffusion models for a few dense perception tasks. However, several crucial design decisions in this process still lack comprehensive justification, encompassing the necessity of the multi-step diffusion mechanism, training strategy, inference ensemble strategy, and fine-tuning data quality. In this work, we conduct a thorough investigation into critical factors that affect transfer efficiency and performance when using diffusion priors. Our key findings are: 1) High-quality fine-tuning data is paramount for both semantic and geometry perception tasks. 2) As a special case of the diffusion scheduler by setting its hyper-parameters, the multi-step generation can be simplified to a one-step fine-tuning paradigm without any loss of performance, while significantly speeding up inference. 3) Apart from fine-tuning the diffusion model with only latent space supervision, task-specific supervision can be beneficial to enhance fine-grained details. These observations culminate in the development of GenPercept, an effective deterministic one-step fine-tuning paradigm tailored for dense visual perception tasks exploiting diffusion priors. Different from the previous multi-step methods, our paradigm offers a much faster inference speed, and can be seamlessly integrated with customized perception decoders and loss functions for task-specific supervision, which can be critical for improving the fine-grained details of predictions. Comprehensive experiments on a diverse set of dense visual perceptual tasks, including monocular depth estimation, surface normal estimation, image segmentation, and matting, are performed to demonstrate the remarkable adaptability and effectiveness of our proposed method. Code: https://github.com/aim-uofa/GenPercept