Common image-to-image translation methods rely on joint training over data from both source and target domains. This excludes cases where domain data is private (e.g., in a federated setting), and often means that a new model has to be trained for a new pair of domains. We present Dual Diffusion Implicit Bridges (DDIBs), an image translation method based on diffusion models, that circumvents training on domain pairs. DDIBs allow translations between arbitrary pairs of source-target domains, given independently trained diffusion models on the respective domains. Image translation with DDIBs is a two-step process: DDIBs first obtain latent encodings for source images with the source diffusion model, and next decode such encodings using the target model to construct target images. Moreover, DDIBs enable cycle-consistency by default and is theoretically connected to optimal transport. Experimentally, we apply DDIBs on a variety of synthetic and high-resolution image datasets, demonstrating their utility in example-guided color transfer, image-to-image translation as well as their connections to optimal transport methods.