Diffusion models have recently shown great potential on many generative tasks.In this work, we explore diffusion models for machine translation (MT).We adapt two prominent diffusion-based text generation models, Diffusion-LM and DiffuSeq, to perform machine translation.As the diffusion models generate non-autoregressively (NAR),we draw parallels to NAR machine translation models.With a comparison to conventional Transformer-based translation models, as well as to the Levenshtein Transformer,an established NAR MT model,we show that the multimodality problem that limits NAR machine translation performance is also a challenge to diffusion models.We demonstrate that knowledge distillation from an autoregressive model improves the performance of diffusion-based MT.A thorough analysis on the translation quality of inputs of different lengths shows that the diffusion models struggle more on long-range dependencies than other models.