In the oil and gas exploration, well logs, the most convenient and economic data source, usually contain missing values due to various reasons. It is crucial to generate accurate synthetic logs for such missing intervals in terms of precise well log interpretation. In this paper, we propose a workflow of generating synthetic logs using cutting-edge machine learning techniques. Unlike existing methods, we exploit a generative model, which can deal with various missing patterns with a single model, and we combine it with a supervised model. With well log data of various regions, we show that our models accurately generate missing logs and outperforms existing supervised-only models. It is expected that our model is beneficial in the real field because of its performance and simplicity.