Few-shot image classification aims at training a model by using only a few (e.g., 5 or even 1) examples of novel classes. The established way of doing so is to rely on a larger set of base data for either pre-training a model, or for training in a meta-learning context. Unfortunately, these approaches often suffer from overfitting since the models can easily memorize all of the novel samples. This paper mitigates this issue and proposes to leverage part of the base data by aligning the novel training instances to the closely related ones in the base training set. This expands the size of the effective novel training set by adding extra related base instances to the few novel ones, thereby allowing to train the entire network. Doing so limits overfitting and simultaneously strengthens the generalization capabilities of the network. We propose two associative alignment strategies: 1) a conditional adversarial alignment loss based on the Wasserstein distance; and 2) a metric-learning loss for minimizing the distance between related base samples and the centroid of novel instances in the feature space. Experiments on two standard datasets demonstrate that combining our centroid-based alignment loss results in absolute accuracy improvements of 4.4%, 1.2%, and 6.0% in 5-shot learning over the state of the art for object recognition, fine-grained classification, and cross-domain adaptation, respectively.