We introduce Persistent Mixture Model (PMM) networks for representation learning in the few-shot image classification context. While previous methods represent classes with a single centroid or rely on post hoc clustering methods, our method learns a mixture model for each base class jointly with the data representation in an end-to-end manner. The PMM training algorithm is organized into two main stages: 1) initial training and 2) progressive following. First, the initial estimate for multi-component mixtures is learned for each class in the base domain using a combination of two loss functions (competitive and collaborative). The resulting network is then progressively refined through a leader-follower learning procedure, which uses the current estimate of the learner as a fixed "target" network. This target network is used to make a consistent assignment of instances to mixture components, in order to increase performance while stabilizing the training. The effectiveness of our joint representation/mixture learning approach is demonstrated with extensive experiments on four standard datasets and four backbones. In particular, we demonstrate that when we combine our robust representation with recent alignment- and margin-based approaches, we achieve new state-of-the-art results in the inductive setting, with an absolute accuracy for 5-shot classification of 82.45% on miniImageNet, 88.20% with tieredImageNet, and 60.70% in FC100, all using the ResNet-12 backbone.