Polygonal road outline extraction from high-resolution aerial images is an important task in large-scale topographic mapping, where roads are represented as vectorized polygons, capturing essential geometric features with minimal vertex redundancy. Despite its importance, no existing method has been explicitly designed for this task. While polygonal building outline extraction has been extensively studied, the unique characteristics of roads, such as branching structures and topological connectivity, pose challenges to these methods. To address this gap, we introduce LDPoly, the first dedicated framework for extracting polygonal road outlines from high-resolution aerial images. Our method leverages a novel Dual-Latent Diffusion Model with a Channel-Embedded Fusion Module, enabling the model to simultaneously generate road masks and vertex heatmaps. A tailored polygonization method is then applied to obtain accurate vectorized road polygons with minimal vertex redundancy. We evaluate LDPoly on a new benchmark dataset, Map2ImLas, which contains detailed polygonal annotations for various topographic objects in several Dutch regions. Our experiments include both in-region and cross-region evaluations, with the latter designed to assess the model's generalization performance on unseen regions. Quantitative and qualitative results demonstrate that LDPoly outperforms state-of-the-art polygon extraction methods across various metrics, including pixel-level coverage, vertex efficiency, polygon regularity, and road connectivity. We also design two new metrics to assess polygon simplicity and boundary smoothness. Moreover, this work represents the first application of diffusion models for extracting precise vectorized object outlines without redundant vertices from remote-sensing imagery, paving the way for future advancements in this field.