Probabilistic denoising diffusion models (DDMs) have set a new standard for 2D image generation. Extending DDMs for 3D content creation is an active field of research. Here, we propose TetraDiffusion, a diffusion model that operates on a tetrahedral partitioning of 3D space to enable efficient, high-resolution 3D shape generation. Our model introduces operators for convolution and transpose convolution that act directly on the tetrahedral partition, and seamlessly includes additional attributes like color. Our design generates mesh geometry much more efficiently: Compared to existing mesh diffusion techniques, TetraDiffusion is up to 200x faster. At the same time, it reduces memory consumption and can operate at substantially higher resolution than existing mesh generators. Using only standard consumer hardware, it sets a new standard in terms of spatial detail and outperforms other mesh generators across a range of quality metrics.