Multi-agent trajectory modeling traditionally focuses on forecasting, often neglecting more general tasks like trajectory completion, which is essential for real-world applications such as correcting tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of heteroscedastic uncertainty. Moreover, popular multi-modal sampling methods lack error probability estimates for each generated scene under the same prior observations, which makes it difficult to rank the predictions at inference time. We introduce U2Diffine, a unified diffusion model built to perform trajectory completion while simultaneously offering state-wise heteroscedastic uncertainty estimates. This is achieved by augmenting the standard denoising loss with the negative log-likelihood of the predicted noise, and then propagating the latent space uncertainty to the real state space using a first-order Taylor approximation. We also propose U2Diff, a faster baseline that avoids gradient computation during sampling. This approach significantly increases inference speed, making it as efficient as a standard generative-only diffusion model. For post-processing, we integrate a Rank Neural Network (RankNN) that enables error probability estimation for each generated mode, demonstrating strong correlation with ground truth errors. Our method outperforms state-of-the-art solutions in both trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), underscoring the effectiveness of our uncertainty and error probability estimation.