Denoising diffusion probabilistic models (DDPMs) have achieved unprecedented success in computer vision. However, they remain underutilized in medical imaging, a field crucial for disease diagnosis and treatment planning. This is primarily due to the high computational cost associated with the use of large number of time steps (e.g., 1,000) in diffusion processes. Training a diffusion model on medical images typically takes days to weeks, while sampling each image volume takes minutes to hours. To address this challenge, we introduce Fast-DDPM, a simple yet effective approach capable of simultaneously improving training speed, sampling speed, and generation quality. Unlike DDPM, which trains the image denoiser across 1,000 time steps, Fast-DDPM trains and samples using only 10 time steps. The key to our method lies in aligning the training and sampling procedures to optimize time-step utilization. Specifically, we introduced two efficient noise schedulers with 10 time steps: one with uniform time step sampling and another with non-uniform sampling. We evaluated Fast-DDPM across three medical image-to-image generation tasks: multi-image super-resolution, image denoising, and image-to-image translation. Fast-DDPM outperformed DDPM and current state-of-the-art methods based on convolutional networks and generative adversarial networks in all tasks. Additionally, Fast-DDPM reduced the training time to 0.2× and the sampling time to 0.01× compared to DDPM. Our code is publicly available at: https://github.com/mirthAI/Fast-DDPM.