Dynamic locomotion of legged robots is a critical yet challenging topic in expanding the operational range of mobile robots. It requires precise planning when possible footholds are sparse, robustness against uncertainties and disturbances, and generalizability across diverse terrains. While traditional model-based controllers excel at planning on complex terrains, they struggle with real-world uncertainties. Learning-based controllers offer robustness to such uncertainties but often lack precision on terrains with sparse steppable areas. Hybrid methods achieve enhanced robustness on sparse terrains by combining both methods but are computationally demanding and constrained by the inherent limitations of model-based planners. To achieve generalized legged locomotion on diverse terrains while preserving the robustness of learning-based controllers, this paper proposes to learn an attention-based map encoding conditioned on robot proprioception, which is trained as part of the end-to-end controller using reinforcement learning. We show that the network learns to focus on steppable areas for future footholds when the robot dynamically navigates diverse and challenging terrains. We synthesize behaviors that exhibit robustness against uncertainties while enabling precise and agile traversal of sparse terrains. Additionally, our method offers a way to interpret the topographical perception of a neural network. We have trained two controllers for a 12-DoF quadrupedal robot and a 23-DoF humanoid robot respectively and tested the resulting controllers in the real world under various challenging indoor and outdoor scenarios, including ones unseen during training.