Deterministic Medical Image Translation via High-fidelity Brownian Bridges

TL;DR

The paper addresses the need for deterministic, high-fidelity medical image translation. It introduces HiFi-BBrg, a dual-mapping framework combining a conditional Brownian bridge generator Γ and a reconstruction cGAN Π, trained with a diffusion loss, fidelity loss, and adversarial loss to ensure reversibility and high fidelity. The forward process follows the Brownian bridge dynamics $dX = -\frac{X-X_T}{1-t}\,dt + 2\sqrt{1-t}\,dW(t)$, and sampling reduces to a deterministic one-step $X_T - \epsilon_\theta(X_T,X_T,T)$, yielding low-variance trajectories. Empirical results on iSEG 2017, BraTS 2018, and Prostate MRI demonstrate state-of-the-art performance in multi-modal translation and multi-image super-resolution, with deterministic outputs. The work highlights potential extensions to unpaired data through bilateral HiFi-BBrg architectures for broader clinical adoption.

Abstract

Recent studies have shown that diffusion models produce superior synthetic images when compared to Generative Adversarial Networks (GANs). However, their outputs are often non-deterministic and lack high fidelity to the ground truth due to the inherent randomness. In this paper, we propose a novel High-fidelity Brownian bridge model (HiFi-BBrg) for deterministic medical image translations. Our model comprises two distinct yet mutually beneficial mappings: a generation mapping and a reconstruction mapping. The Brownian bridge training process is guided by the fidelity loss and adversarial training in the reconstruction mapping. This ensures that translated images can be accurately reversed to their original forms, thereby achieving consistent translations with high fidelity to the ground truth. Our extensive experiments on multiple datasets show HiFi-BBrg outperforms state-of-the-art methods in multi-modal image translation and multi-image super-resolution.

Figures (4)

• Figure 1: Other diffusive bridge models (e.g., bbdm and abridge) vs. HiFi-BBrg. Up: Image translation from domain $\mathcal{A}$ to $\mathcal{B}$ through sampling. Bottom: One time-step sampling in HiFi-BBrg provides completely deterministic results.
• Figure 2: HiFi-BBrg architecture illustration. The conditional Brownian bridge $\epsilon_\theta$ maps from $\mathcal{A}$ to $\mathcal{B}$, while the conditional generator $G$ maps from $\mathcal{B}$ to $\mathcal{A}$. The adversarial training is performed using the discriminator $D$ to distinguish between the real image $X_T$ and its reconstruction $\hat{X}^t_T$.
• Figure 3: Comparison of HiFi-BBrg and SOTA Methods on the BraTS2018 T1-W to T2-W Image Translation Dataset. The images generated by Fast-DDPM method were sampled five times, resulting in a std. of 0.0072.
• Figure 4: Comparison between HiFi-BBrg and SOTA methods on the Prostate MRI super-resolution dataset. The images generated by Fast-DDPM method were sampled five times, resulting in a std. of 0.0104. Two samples are shown with an absolute difference plot highlighting variations due to the non-deterministic approach.