In this work, we propose a new statistical model for building robust dialog systems using neural networks to either retrieve or generate dialog response based on an existing data sources. In the retrieval task, we propose an approach that uses paraphrase identification during the retrieval process. This is done by employing recursive autoencoders and dynamic pooling to determine whether two sentences with arbitrary length have the same meaning. For both the generation and retrieval tasks, we propose a model using long short term memory (LSTM) neural networks that works by first using an LSTM encoder to read in the user's utterance into a continuous vector-space representation, then using an LSTM decoder to generate the most probable word sequence. An evaluation based on objective and subjective metrics shows that the new proposed approaches have the ability to deal with user inputs that are not well covered in the database compared to standard example-based dialog baselines.