Pre-trained language models (LMs) are used for knowledge intensive tasks like question answering, but their knowledge gets continuously outdated as the world changes. Prior work has studied targeted updates to LMs, injecting individual facts and evaluating whether the model learns these facts while not changing predictions on other contexts. We take a step forward and study LMs’ abilities to make inferences based on injected facts (or propagate those facts): for example, after learning that something is a TV show, does an LM predict that you can watch it? We study this with two cloze-style tasks: an existing dataset of real-world sentences about novel entities (ECBD) as well as a new controlled benchmark with manually designed templates requiring varying levels of inference about injected knowledge. Surprisingly, we find that existing methods for updating knowledge (gradient-based fine-tuning and modifications of this approach) show little propagation of injected knowledge. These methods improve performance on cloze instances only when there is lexical overlap between injected facts and target inferences. Yet, prepending entity definitions in an LM’s context improves performance across all settings, suggesting that there is substantial headroom for parameter-updating approaches for knowledge injection.