  We propose a novel unpaired image-to-image translation method that uses
denoising diffusion probabilistic models without requiring adversarial
training. Our method, UNpaired Image Translation with Denoising Diffusion
Probabilistic Models (UNIT-DDPM), trains a generative model to infer the joint
distribution of images over both domains as a Markov chain by minimising a
denoising score matching objective conditioned on the other domain. In
particular, we update both domain translation models simultaneously, and we
generate target domain images by a denoising Markov Chain Monte Carlo approach
that is conditioned on the input source domain images, based on Langevin
dynamics. Our approach provides stable model training for image-to-image
translation and generates high-quality image outputs. This enables
state-of-the-art Fr\'echet Inception Distance (FID) performance on several
public datasets, including both colour and multispectral imagery, significantly
outperforming the contemporary adversarial image-to-image translation methods.
