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. Unlike traditional terrestrial networks, LAENets are characterized by control mechanisms and ever-changing operational factors, which make them more complex and susceptible to vulnerabilities. As applications of LAENet continue to expand, robustness of these systems becomes crucial. In this paper, we investigate a novel application of Generative Artificial Intelligence (GenAI) to improve the robustness of 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 Expert (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 44% increase in the worst-case achievable secrecy rate. These findings highlight the significant potential of GenAI in strengthening LAENet robustness.