Generative steganography is the process of hiding secret messages in generated images instead of cover images. Existing studies on generative steganography use GAN or Flow models to obtain high hiding message capacity and anti-detection ability over cover images. However, they create relatively unrealistic stego images because of the inherent limitations of generative models. We propose Diffusion-Stego, a generative steganography approach based on diffusion models which outperform other generative models in image generation. Diffusion-Stego projects secret messages into latent noise of diffusion models and generates stego images with an iterative denoising process. Since the naive hiding of secret messages into noise boosts visual degradation and decreases extracted message accuracy, we introduce message projection, which hides messages into noise space while addressing these issues. We suggest three options for message projection to adjust the trade-off between extracted message accuracy, anti-detection ability, and image quality. Diffusion-Stego is a training-free approach, so we can apply it to pre-trained diffusion models which generate high-quality images, or even large-scale text-to-image models, such as Stable diffusion. Diffusion-Stego achieved a high capacity of messages (3.0 bpp of binary messages with 98% accuracy, and 6.0 bpp with 90% accuracy) as well as high quality (with a FID score of 2.77 for 1.0 bpp on the FFHQ 64$\times$64 dataset) that makes it challenging to distinguish from real images in the PNG format.