Multi-agent trajectory modeling has primarily focused on forecasting future states, often overlooking broader tasks like trajectory completion, which are crucial for real-world applications such as correct tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of uncertainty. Moreover, popular multi-modal sampling methods lack any error probability estimates for each generated scene under the same prior observations, making it difficult to rank the predictions during inference time. We introduce U2Diff, a unified diffusion model designed to handle trajectory completion while providing state-wise uncertainty estimates jointly. This uncertainty estimation is achieved by augmenting the simple denoising loss with the negative log-likelihood of the predicted noise and propagating latent space uncertainty to the real state space. Additionally, we incorporate a Rank Neural Network in post-processing to enable error probability estimation for each generated mode, demonstrating a strong correlation with the error relative to ground truth. Our method outperforms the state-of-the-art solutions in trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), highlighting the effectiveness of uncertainty and error probability estimation.