In the field of Automated Planning there is often the need for a set of planning problems from a particular domain, e.g., to be used as training data for Machine Learning or as benchmarks in planning competitions. In most cases, these problems are created either by hand or by a domain-specific generator, putting a burden on the human designers. In this paper we propose NeSIG, to the best of our knowledge the first domain-independent method for automatically generating planning problems that are valid, diverse and difficult to solve. We formulate problem generation as a Markov Decision Process and train two generative policies with Deep Reinforcement Learning to generate problems with the desired properties. We conduct experiments on several classical domains, comparing our method with handcrafted domain-specific generators that generate valid and diverse problems but do not optimize difficulty. The results show NeSIG is able to automatically generate valid problems of greater difficulty than the competitor approaches, while maintaining good diversity.