Edge AI-driven diffusion models (DMs) are increasingly integrated into consumer devices for high-quality data generation and content creation. This paper introduces InvisibleDiffusion, a novel backdoor attack framework for diffusion models in consumer electronics, designed to remain undetected by utilizing a non-standard Gaussian distribution as a concealed trigger. Unlike previous backdoor methods, InvisibleDiffusion does not rely on obvious visual triggers, enhancing its stealthiness. Extensive experiments demonstrate that InvisibleDiffusion achieves high attack efficacy against DDPM and DDIM models on CIFAR-10 and CelebA datasets, while maintaining the functional integrity of the models. Our code is available for reproducibility at https://anonymous.4open.science/r/b2hoaWNhbnRzZWV0aGF0bm9vb29vb29vb29v.