Self-consistent recursive diffusion bridge for medical image translation

Abstract

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.