Abstract: Despite the growing interest in continual learning, most of its contemporary works have been studied in a rather restricted setting where tasks are clearly distinguishable, and task boundaries are known during training. However, if our goal is to develop an algorithm that learns as humans do, this setting is far from realistic, and it is essential to develop a methodology that works in a task-free manner. Meanwhile, among several branches of continual learning, expansion-based methods have the advantage of eliminating catastrophic forgetting by allocating new resources to learn new data. In this work, we propose an expansion-based approach for task-free continual learning. Our model, named Continual Neural Dirichlet Process Mixture (CN-DPM), consists of a set of neural network experts that are in charge of a subset of the data. CN-DPM expands the number of experts in a principled way under the Bayesian nonparametric framework. With extensive experiments, we show that our model successfully performs task-free continual learning for both discriminative and generative tasks such as image classification and image generation.