Multi-instance learning is a type of weakly supervised learning. It deals with tasks where the data is a set of bags and each bag is a set of instances. Only the bag labels are observed whereas the labels for the instances are unknown. An important advantage of multi-instance learning is that by representing objects as a bag of instances, it is able to preserve the inherent dependencies among parts of the objects. Unfortunately, most existing algorithms assume all instances to be identically and independently distributed, which violates real-world scenarios since the instances within a bag are rarely independent. In this work, we propose the Multi-Instance Variational Autoencoder (MIVAE) algorithm which explicitly models the dependencies among the instances for predicting both bag labels and instance labels. Experimental results on several multi-instance benchmarks and end-to-end medical imaging datasets demonstrate that MIVAE performs better than state-of-the-art algorithms for both instance label and bag label prediction tasks.