Synthesizing realistic animations of humans, animals, and even imaginary creatures, has long been a goal for artists and computer graphics professionals. Compared to the imaging domain, which is rich with large available datasets, the number of data instances for the motion domain is limited, particularly for the animation of animals and exotic creatures (e.g., dragons), which have unique skeletons and motion patterns. In this work, we introduce SinMDM, a Single Motion Diffusion Model. It is designed to learn the internal motifs of a single motion sequence with arbitrary topology and synthesize a variety of motions of arbitrary length that remain faithful to the learned motifs. We harness the power of diffusion models and present a denoising network explicitly designed for the task of learning from a single input motion. SinMDM is crafted as a lightweight architecture, which avoids overfitting by using a shallow network with local attention layers that narrow the receptive field and encourage motion diversity. Our work applies to multiple contexts, including spatial and temporal in-betweening, motion expansion, style transfer, and crowd animation. Our results show that SinMDM outperforms existing methods both qualitatively and quantitatively. Moreover, while prior network-based approaches require additional training for different applications, SinMDM supports these applications during inference. Our project page, which includes links to the code and trained models, is accessible at https://sinmdm.github.io/SinMDM-page.