Denoising diffusion generative models are capable of generating high-quality data, but suffers from the computation-costly generation process, due to a iterative noise estimation using full-precision networks. As an intuitive solution, quantization can significantly reduce the computational and memory consumption by low-bit parameters and operations. However, low-bit noise estimation networks in diffusion models (DMs) remain unexplored yet and perform much worse than the full-precision counterparts as observed in our experimental studies. In this paper, we first identify that the bottlenecks of low-bit quantized DMs come from a large distribution oscillation on activations and accumulated quantization error caused by the multi-step denoising process. To address these issues, we first develop a Timestep-aware Quantization (TaQ) method and a Noise-estimating Mimicking (NeM) scheme for low-bit quantized DMs (Q-DM) to effectively eliminate such oscillation and accumulated error respectively, leading to well-performed low-bit DMs. In this way, we propose an efficient Q-DM to calculate low-bit DMs by considering both training and inference process in the same framework. We evaluate our methods on popular DDPM and DDIM models. Extensive experimental results show that our method achieves a much better performance than the prior arts. For example, the 4-bit Q-DM theoretically accelerates the 1000-step DDPM by 7.8x and achieves a FID score of 5.17, on the unconditional CIFAR-10 dataset.