Accurate precipitation forecasts are crucial for applications such as flood management, agricultural planning, water resource allocation, and weather warnings. Despite advances in numerical weather prediction (NWP) models, they still exhibit significant biases and uncertainties, especially at high spatial and temporal resolutions. To address these limitations, we explore uncertainty-aware deep learning models for post-processing daily cumulative quantitative precipitation forecasts to obtain forecast uncertainties that lead to a better trade-off between accuracy and reliability. Our study compares different state-of-the-art models, and we propose a variant of the well-known SDE-Net, called SDE U-Net, tailored to segmentation problems like ours. We evaluate its performance for both typical and intense precipitation events.Our results show that all deep learning models significantly outperform the average baseline NWP solution, with our implementation of the SDE U-Net showing the best trade-off between accuracy and reliability. Integrating these models, which account for uncertainty, into operational forecasting systems can improve decision-making and preparedness for weather-related events.