Fast urban pluvial flood models are necessary for a range of applications, such as near real-time flood nowcasting or processing large rainfall ensembles for uncertainty analysis. Data-driven models can help overcome the long computational time of traditional flood simulation models, and the state-of-the-art models have shown promising accuracy. Yet the lack of generalizability of data-driven urban pluvial flood models to both unseen rainfall and distinctively different terrain, at the fine resolution required for urban flood mapping, still limits their application. These models usually adopt a patch-based framework to overcome multiple bottlenecks, such as data availability and computational and memory constraints. However, this approach does not incorporate contextual information of the terrain surrounding the small image patch (typically 256m × 256m). We propose a new deep-learning model that maintains the high-resolution information of the local patch and incorporates a larger surrounding area to increase the visual field of the model with the aim of enhancing the generalizability of data-driven urban pluvial flood models. We trained and tested the model in the city of Zurich (Switzerland), at a spatial resolution of 1 m, for 1 h rainfall events at 5 min temporal resolution. We demonstrate that our model can faithfully represent flood depths for a wide range of rainfall events, with peak rainfall intensities ranging from 42.5 to 161.4mmh^-1. Then, we assessed the model's terrain generalizability in distinct urban settings, namely, Lucerne (Switzerland) and Singapore. The model accurately identifies locations of water accumulation, which constitutes an improvement compared to other deep-learning models. Using transfer learning, the model was successfully retrained in the new cities, requiring only a single rainfall event to adapt the model to new terrains while preserving adaptability across diverse rainfall conditions. Our results indicate that by incorporating contextual terrain information into the local patches, our proposed model effectively simulates high-resolution urban pluvial flood maps, demonstrating applicability across varied terrains and rainfall events.