Neural information retrieval often adopts a retrieve-and-rerank framework: a bi-encoder network first retrieves K (e.g., 100) candidates that are then re-ranked using a more powerful cross-encoder model to rank the better candidates higher. The re-ranker generally produces better candidate scores than the retriever, but is limited to seeing only the top K retrieved candidates, thus providing no improvements in retrieval performance as measured by Recall@K. In this work, we leverage the re-ranker to also improve retrieval by providing inference-time relevance feedback to the retriever. Concretely, we update the retriever's query representation for a test instance using a lightweight inference-time distillation of the re-ranker's prediction for that instance. The distillation loss is designed to bring the retriever's candidate scores closer to those of the re-ranker. A second retrieval step is then performed with the updated query vector. We empirically show that our approach, which can serve arbitrary retrieve-and-rerank pipelines, significantly improves retrieval recall in multiple domains, languages, and modalities.