Modern machine learning models usually do not extrapolate well, i.e., they often have high prediction errors in the regions of sample space lying far from the training data. In high dimensional spaces detecting out-of-distribution points becomes a non-trivial problem. Thus, uncertainty estimation for model predictions becomes crucial for the successful application of machine learning models in many applications. In this work, we show that increasing the diversity of realizations sampled from a neural network with dropout helps to improve the quality of uncertainty estimation. In a series of experiments on simulated and real-world data, we demonstrate that diversification via determinantal point processes-based sampling allows achieving state-of-the-art results in uncertainty estimation for regression and classification tasks. Importantly, our approach does not require any modification to the models or training procedures, allowing for straightforward application to any deep learning model with dropout layers.