<p>We propose a new methodology for building stochastic models of commodity prices based on the probabilistic predictions of a suitably designed and trained deep neural network (DNN). Our method directly generates probabilistic paths, capturing the main features of market price dynamics such as mean-reversion and extreme movements without requiring complex parameter estimation techniques. To reproduce the main stylized facts of the commodity price dynamics, a suitable DNN architecture and an innovative training procedure are proposed. Our findings show that our DNN-based approach is highly effective in capturing mean-reversion effects, extreme price movements, and other nonlinearities of the dynamics. A comparison is proposed on natural gas market prices observed at the Henry Hub between the DNN-based model and a suitable regime-switching hidden Markov model. Comparative experiments show that the DNN-based model provides similar or superior performance in terms of statistical accuracy and predictive reliability.</p>