Modern deep neural networks are often too large to use in many practical scenarios. Neural network pruning is an important technique for reducing the size of such models and accelerating inference. Gibbs pruning is a novel framework for expressing and designing neural network pruning methods. Combining approaches from statistical physics and stochastic regularization methods, it can train and prune a network simultaneously in such a way that the learned weights and pruning mask are well-adapted for each other. It can be used for structured or unstructured pruning and we propose a number of specific methods for each. We compare our proposed methods to a number of contemporary neural network pruning methods and find that Gibbs pruning outperforms them. In particular, we achieve a new state-of-the-art result for pruning ResNet-56 with the CIFAR-10 dataset.