Recent works have demonstrated that natural language can be used to generate and edit 3D shapes. However, these methods generate shapes with limited fidelity and diversity. We introduce CLIP-Sculptor, a method to address these constraints by producing high-fidelity and diverse 3D shapes without the need for (text, shape) pairs during training. CLIP-Sculptor achieves this in a multi-resolution approach that first generates in a low-dimensional latent space and then upscales to a higher resolution for improved shape fidelity. For improved shape diversity, we use a discrete latent space which is modeled using a transformer conditioned on CLIP’s image-text embedding space. We also present a novel variant of classifier-free guidance, which improves the accuracy-diversity trade-off. Finally, we perform extensive experiments demonstrating that CLIP-Sculptor outperforms state-of-the-art baselines.