Coding algorithms usually compress independently the images of a collection, in particular when the correlation between them only resides at the semantic level, i.e., information related to the high-level image content. In this work, we propose a coding solution able to exploit this semantic redundancy to decrease the storage cost of data collections. First we introduce the multi-item compression framework. Then we derive a loss term to shape the latent space of a variational auto-encoder so that the latent vectors of semantically identical images can be aligned. Finally, we experimentally demonstrate that this alignment leads to a more compact representation of the data collection.