Dynamically integrating new or rapidly evolving information after Language Model (LM) pre-training remains challenging, particularly in low-data scenarios or when dealing with private and specialized documents. In-context learning and retrieval-augmented generation (RAG) face limitations, including their high inference costs and their inability to capture global document information. In this paper, we propose a way of modularizing knowledge by training Knowledge Modules (KMs). KMs are lightweight components implemented as parameter-efficient LoRA modules, which are trained to store information about new documents and can be easily plugged into models on demand. We show that next-token prediction performs poorly in training KMs. We instead propose Deep Context Distillation: we learn KMs parameters such as to simulate hidden states and logits of a teacher that takes the document in context. Our method outperforms standard next-token prediction and pre-instruction training techniques, across two datasets. Finally, we highlight synergies between KMs and retrieval-augmented generation.