Electronic Health Records (EHRs) provide vital contextual information to radiologists and other physicians when making a diagnosis. Unfortunately, because a given patient's record may contain hundreds of notes and reports, identifying relevant information within these in the short time typically allotted to a case is very difficult. We propose and evaluate models that extract relevant text snippets from patient records to provide a rough case summary intended to aid physicians considering one or more diagnoses. This is hard because direct supervision (i.e., physician annotations of snippets relevant to specific diagnoses in medical records) is prohibitively expensive to collect at scale. We propose a distantly supervised strategy in which we use groups of International Classification of Diseases (ICD) codes observed in 'future' records as noisy proxies for 'downstream' diagnoses. Using this we train a transformer-based neural model to perform extractive summarization conditioned on potential diagnoses. This model defines an attention mechanism that is conditioned on potential diagnoses (queries) provided by the diagnosing physician. We train (via distant supervision) and evaluate variants of this model on EHR data from Brigham and Women's Hospital in Boston and MIMIC-III (the latter to facilitate reproducibility). Evaluations performed by radiologists demonstrate that these distantly supervised models yield better extractive summaries than do unsupervised approaches. Such models may aid diagnosis by identifying sentences in past patient reports that are clinically relevant to a potential diagnosis.