  Denoising diffusion models (DDM) have gained recent traction in medical image
translation given improved training stability over adversarial models. DDMs
learn a multi-step denoising transformation to progressively map random
Gaussian-noise images onto target-modality images, while receiving stationary
guidance from source-modality images. As this denoising transformation diverges
significantly from the task-relevant source-to-target transformation, DDMs can
suffer from weak source-modality guidance. Here, we propose a novel
self-consistent recursive diffusion bridge (SelfRDB) for improved performance
in medical image translation. Unlike DDMs, SelfRDB employs a novel forward
process with start- and end-points defined based on target and source images,
respectively. Intermediate image samples across the process are expressed via a
normal distribution with mean taken as a convex combination of start-end
points, and variance from additive noise. Unlike regular diffusion bridges that
prescribe zero variance at start-end points and high variance at mid-point of
the process, we propose a novel noise scheduling with monotonically increasing
variance towards the end-point in order to boost generalization performance and
facilitate information transfer between the two modalities. To further enhance
sampling accuracy in each reverse step, we propose a novel sampling procedure
where the network recursively generates a transient-estimate of the target
image until convergence onto a self-consistent solution. Comprehensive analyses
in multi-contrast MRI and MRI-CT translation indicate that SelfRDB offers
superior performance against competing methods.
