A Self-supervised Diffusion Bridge for MRI Reconstruction

TL;DR

SelfDB addresses the lack of ground-truth images for training diffusion bridges by introducing a self-supervised diffusion process over two degradation operators, including an intermediate sub-sampling $\overline{\bm M}$, and training a network to map intermediate measurements $y_t$ to the full measurement $y$ using only $y$ as the target. The method defines $y_t=(1-t)\overline{\bm M}{\bm y}+t{\bm M'}{\bm y}+\sigma_t\epsilon$ and optimizes $ \mathbb{E}_{\bm y,\epsilon,t,\bm y_t}[\|{\bm M}{\bm A}f_\theta(y_t,t)-\bm y\|_2^2]$, enabling a diffusion bridge that progressively incorporates information from $\overline{\bm M}{\bm y}$. In CS-MRI, SelfDB outperforms Ambient-DB and C-Ambient-DDM in distortion and perceptual metrics, while offering a tunable perception-distortion trade-off via the number of inference steps. This advancement enables fast, measurement-consistent reconstructions without ground-truth images, broadening the applicability of diffusion-bridge methods to real-world inverse problems.

Abstract

Diffusion bridges (DBs) are a class of diffusion models that enable faster sampling by interpolating between two paired image distributions. Training traditional DBs for image reconstruction requires high-quality reference images, which limits their applicability to settings where such references are unavailable. We propose SelfDB as a novel self-supervised method for training DBs directly on available noisy measurements without any high-quality reference images. SelfDB formulates the diffusion process by further sub-sampling the available measurements two additional times and training a neural network to reverse the corresponding degradation process by using the available measurements as the training targets. We validate SelfDB on compressed sensing MRI, showing its superior performance compared to the denoising diffusion models.

Figures (2)

• Figure 1: Visual comparisons of Ambient-DB, conditional ambient diffusion (C-Ambient-DDM), and the proposed SelfDB. C-Ambient-DDM is an existing self-supervised approach for denoising diffusion models, while Ambient-DB is its direct extension into the DB framework. NRMSE and LPIPS values for each method are labeled in the top-left corner of the images. Note how SelfDB yields images with details closely matching the reference, highlighted by the read arrow in the zoomed-in region.
• Figure 2: Visual results of SelfDB with different inference steps. Best viewed in digital format. This figure demonstrates that SelfDB empirically provides a perception-distortion trade-off. Notably, perceptual quality (LPIPS) improves as the number of inference steps increases, while distortion with respect to the reference (NRMSE) also rises.