Low-Altitude Economy Networks (LAENets) have emerged as significant enablers of social activities, offering low-altitude services such as the transportation of packages, groceries, and medical supplies. Owing to their control mechanisms and ever-changing operational factors, LAENets are inherently more complex and vulnerable to security threats than traditional terrestrial networks. As applications of LAENet continue to expand, the robustness of these systems becomes crucial. In this paper, we propose a generative artificial intelligence (GenAI) optimization framework that tackles robustness challenges in LAENets. We conduct a systematic analysis of robustness requirements for LAENets, complemented by a comprehensive review of robust Quality of Service (QoS) metrics from the wireless physical layer perspective. We then investigate existing GenAI-enabled approaches for robustness enhancement. This leads to our proposal of a novel diffusion-based optimization framework with a Mixture of Experts (MoE)-transformer actor network. In the robust beamforming case study, the proposed framework demonstrates its effectiveness by optimizing beamforming under uncertainties, achieving a more than 15% increase over four learning baselines in the worst-case achievable secrecy rate. These findings highlight the significant potential of GenAI in strengthening LAENet robustness.