Self-consistent recursive diffusion bridge for medical image translation

Denoising diffusion models (DDM) have gained recent traction in medical image translation given their high training stability and image fidelity. DDMs learn a multi-step denoising transformation that progressively maps random Gaussian-noise images provided as input onto target-modality images as output, while receiving indirect guidance from source-modality images via a separate static channel. This denoising transformation diverges significantly from the task-relevant source-to-target modality transformation, as source images are governed by a non-noise distribution. In turn, DDMs can suffer from suboptimal source-modality guidance and performance losses in medical image translation. Here, we propose a novel self-consistent recursive diffusion bridge (SelfRDB) that leverages direct source-modality guidance within its diffusion process for improved performance in medical image translation. Unlike DDMs, SelfRDB devises a novel forward process with the start-point taken as the target image, and the end-point defined based on the source image. Intermediate image samples across the process are expressed via a normal distribution whose mean is taken as a convex combination of start-end points, and whose variance is controlled by additive noise. Unlike regular diffusion bridges that prescribe zero noise variance at start-end points and high noise variance at mid-point of the process, we propose a novel noise scheduling with monotonically increasing variance towards the end-point in order to facilitate information transfer between the two modalities and boost robustness against measurement noise. 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 experiments in multi-contrast MRI and MRI-CT translation indicate that SelfRDB achieves state-of-the-art results in terms of image quality.