Fringe projection profilometry-based 3-D reconstruction of objects with high reflectivity and low surface roughness remains a significant challenge. When measuring such glossy surfaces, specular reflection and indirect illumination often lead to severe distortion or loss of the projected fringe patterns. To address these issues, we propose a latent diffusion-based structured light for reflective objects (LD-SLRO). Phase-shifted fringe images captured from highly reflective surfaces are first encoded to extract latent representations that capture surface reflectance characteristics. These latent features are then used as conditional inputs to a latent diffusion model, which probabilistically suppresses reflection-induced artifacts and recover lost fringe information, yielding high-quality fringe images. The proposed components, including the specular reflection encoder, time-variant channel affine layer, and attention modules, further improve fringe restoration quality. In addition, LD-SLRO provides high flexibility in configuring the input and output fringe sets. Experimental results demonstrate that the proposed method improves both fringe quality and 3-D reconstruction accuracy over state-of-the-art methods, reducing the average root-mean-squared error from 1.8176 mm to 0.9619 mm.