In this work, we present DiffVoice, a novel text-to-speech model based on latent diffusion. We propose to first encode speech signals into a phoneme-rate latent representation with a variational autoencoder enhanced by adversarial training, and then jointly model the duration and the latent representation with a diffusion model. Subjective evaluations on LJSpeech and LibriTTS datasets demonstrate that our method beats the best publicly available systems in naturalness. By adopting recent generative inverse problem solving algorithms for diffusion models, DiffVoice achieves the state-of-the-art performance in text-based speech editing, and zero-shot adaptation.