Although neural text-to-speech (TTS) models have attracted a lot of attention and succeeded in generating human-like speech, there is still room for improvements to its naturalness and architectural efficiency. In this work, we propose a novel non-autoregressive TTS model, namely Diff-TTS, which achieves highly natural and efficient speech synthesis. Given the text, Diff-TTS exploits a denoising diffusion framework to transform the noise signal into a mel-spectrogram via diffusion time steps. In order to learn the mel-spectrogram distribution conditioned on the text, we present a likelihood-based optimization method for TTS. Furthermore, to boost up the inference speed, we leverage the accelerated sampling method that allows Diff-TTS to generate raw waveforms much faster without significantly degrading perceptual quality. Through experiments, we verified that Diff-TTS generates 28 times faster than the real-time with a single NVIDIA 2080Ti GPU.