Climate change is intensifying rainfall extremes, making high-resolution precipitation projections crucial for society to better prepare for impacts such as flooding. However, current Global Climate Models (GCMs) operate at spatial resolutions too coarse for localized analyses. To address this limitation, deep learning-based statistical downscaling methods offer promising solutions, providing high-resolution precipitation projections with a moderate computational cost. In this work, we introduce a bias-informed conditional diffusion model for statistical downscaling of precipitation. Specifically, our model leverages a conditional diffusion approach to learn distribution priors from large-scale, high-resolution precipitation datasets. The long-tail distribution of precipitation poses a unique challenge for training diffusion models; to address this, we apply gamma correction during preprocessing. Additionally, to correct biases in the downscaled results, we employ a guided-sampling strategy to enhance bias correction. Our experiments demonstrate that the proposed model achieves highly accurate results in an 8 times downscaling setting, outperforming previous deterministic methods. The code and dataset are available at https://github.com/RoseLV/research_super-resolution