Diffusion models have achieved great success in synthesizing diverse and high-fidelity images. However, sampling speed and memory constraints remain a major barrier to the practical adoption of diffusion models, since the generation process for these models can be slow due to the need for iterative noise estimation using compute-intensive neural networks. We propose to tackle this problem by compressing the noise estimation network to accelerate the generation process through post-training quantization (PTQ). While existing PTQ approaches have not been able to effectively deal with the changing output distributions of noise estimation networks in diffusion models over multiple time steps, we are able to formulate a PTQ method that is specifically designed to handle the unique multi-timestep structure of diffusion models with a data calibration scheme using data sampled from different time steps. Experimental results show that our proposed method is able to directly quantize full-precision diffusion models into 8-bit or 4-bit models while maintaining comparable performance in a training-free manner, achieving a FID change of at most 1.88. Our approach can also be applied to text-guided image generation, and for the first time we can run stable diffusion in 4-bit weights without losing much perceptual quality, as shown in Figure 5 and Figure 9.