High-order Gaussian beams with multiple propagation modes have been studied for free-space optical communications. Fast classification of beams using a diffractive deep neural network (D2NN) has been proposed. D2NN optimization is important because it has numerous hyperparameters, such as interlayer distances and mode combinations. In this study, we classify Hermite-Gaussian beams, which are high-order Gaussian beams, using a D2NN, and automatically tune one of its hyperparameters known as the interlayer distance. We used the tree-structured Parzen estimator, a hyperparameter auto-tuning algorithm, to search for the best model. As a result, the proposed method improved the classification accuracy in a 16 mode classification from 98.3% in the case of equal spacing of layers to 98.8%. In a 36 mode classification, the proposed method significantly improved the classification accuracy from 84.9% to 94.9%. In addition, we confirmed that accuracy by auto-tuning improves as the number of classification modes increases.