Recent work has demonstrated the significant potential of denoising diffusion modelsfor generating human motion, including text-to-motion capabilities.However, these methods are restricted by the paucity of annotated motion data,a focus on single-person motions, and a lack of detailed control.In this paper, we introduce three forms of composition based on diffusion priors:sequential, parallel, and model composition.Using sequential composition, we tackle the challenge of long sequencegeneration. We introduce DoubleTake, an inference-time method with whichwe generate long animations consisting of sequences of prompted intervalsand their transitions, using a prior trained only for short clips.Using parallel composition, we show promising steps toward two-person generation.Beginning with two fixed priors as well as a few two-person training examples, we learn a slimcommunication block, ComMDM, to coordinate interaction between the two resulting motions.Lastly, using model composition, we first train individual priorsto complete motions that realize a prescribed motion for a given joint.We then introduce DiffusionBlending, an interpolation mechanism to effectively blend severalsuch models to enable flexible and efficient fine-grained joint and trajectory-level control and editing.We evaluate the composition methods using an off-the-shelf motion diffusion model,and further compare the results to dedicated models trained for these specific tasks.