Global flood risk has increased due to worsening extreme weather events and human migration into growing flood-prone areas. Accurate, high-resolution, and near-real time flood maps can address flood risk by reducing financial loss and damage. We propose Model to Map, a novel machine learning approach that utilizes bi-temporal context to improve flood water segmentation performance for Sentinel-1 imagery. We show that the inclusion of unflooded context for the area, or "memory," allows the model to tap into a "prior state" of pre-flood conditions, increasing performance in geographic regions in which single-image radar-based flood mapping methods typically underperform (e.g. deserts). We focus on accuracy across different biomes to ensure global performance. Our experiments and novel data processing technique show that the confluence of pre-flood and permanent water context provides a 21% increase in mIoU over the baseline overall, and over 87% increase in deserts.