  Common image-to-image translation methods rely on joint training over data
from both source and target domains. The training process requires concurrent
access to both datasets, which hinders data separation and privacy protection;
and existing models cannot be easily adapted for translation of new domain
pairs. We present Dual Diffusion Implicit Bridges (DDIBs), an image translation
method based on diffusion models, that circumvents training on domain pairs.
Image translation with DDIBs relies on two diffusion models trained
independently on each domain, and is a two-step process: DDIBs first obtain
latent encodings for source images with the source diffusion model, and then
decode such encodings using the target model to construct target images. Both
steps are defined via ordinary differential equations (ODEs), thus the process
is cycle consistent only up to discretization errors of the ODE solvers.
Theoretically, we interpret DDIBs as concatenation of source to latent, and
latent to target Schrodinger Bridges, a form of entropy-regularized optimal
transport, to explain the efficacy of the method. Experimentally, we apply
DDIBs on synthetic and high-resolution image datasets, to demonstrate their
utility in a wide variety of translation tasks and their inherent optimal
transport properties.
