In this paper, a novel semantic communication framework empowered by generative artificial intelligence (GAI) is proposed, to enhance the robustness against both channel noise and transmission data distribution shifts. A theoretical foundation is established using stochastic differential equations (SDEs), from which a closed-form mapping between any signal-to-noise ratio (SNR) and the optimal denoising timestep is derived. Moreover, to address distribution mismatch, a mathematical scaling method is introduced to align received semantic features with the training distribution of the GAI. Built on this theoretical foundation, a latent diffusion model (LDM)-based semantic communication framework is proposed that combines a variational autoencoder for semantic features extraction, where a pretrained diffusion model is used for denoising. The proposed system is a training-free framework that supports zero-shot generalization, and achieves superior performance under low-SNR and out-of-distribution conditions, offering a scalable and robust solution for future 6G semantic communication systems. Experimental results demonstrate that the proposed semantic communication framework achieves state-of-the-art performance in both pixel-level accuracy and semantic perceptual quality, consistently outperforming baselines across a wide range of SNRs and data distributions without any fine-tuning or post-training.