GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance

Diffusion bridge models offer a powerful framework for connecting two data distributions, such as in image restoration and translation. Many existing methods learn this bridge by mimicking the score-matching formulation of standard diffusion models. In this work, we find that this way leads to an anomalous underfitting phenomenon near the target endpoint, as the process approaches the target distribution ($t \to 0$). This underfitting, characterized by significant drift in the predicted variance and direction, results from an excessively large discrepancy in noise levels between the network's input and its regression target.To resolve this issue, we propose the Noise-Aligned Diffusion Bridge (NADB).Our approach reformulates the diffusion bridge by first employing a mean network to provide a cleaner conditional target, and then introducing a novel, noise-aligned mapping relationship. This new formulation resolves the noise mismatch and corrects the underfitting near the target endpoint. Experimental validation across multiple image restoration and image translation tasks demonstrates the effectiveness of our approach. Code is available at https://github.com/gyr02/NADB.

Diffusion bridge models leverage Doob's $h$-transform to construct stochastic transports between arbitrary endpoint distributions, and have shown strong potential in image-to-image translation and restoration. However, most existing bridge models rely on hard endpoint conditioning, which forces the terminal state to match a prescribed target exactly. This hard constraint induces terminal-boundary singularities: the terminal law collapses to a Dirac measure, and the resulting drift coefficients become ill-conditioned near the endpoint. In this paper, we propose Soft Denoising Diffusion Bridge Models (SDDBMs), a generalized framework that regularizes diffusion bridges directly at the level of their terminal constraints. Instead of imposing an exact endpoint, SDDBMs prescribe a non-degenerate Gaussian terminal marginal under the transformed path measure, with a flexible terminal center and variance. Starting from this prescribed marginal, we develop a complete closed-form construction of the soft bridge, including the Gaussian terminal reweighting and soft $h$-function, the induced Gaussian forward marginals and $\mathbf{x}_0$-free dynamics. Theoretically, SDDBMs provide a unified probabilistic perspective that encompasses existing diffusion bridge models, including DDBMs, GOUB, and UniDB, as special cases under specific parameter choices. Extensive experiments on image restoration tasks demonstrate that SDDBMs achieve improved numerical stability and superior generation quality over existing bridge-based methods.

Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully paired datasets, thereby imposing a single data-driven constraint. We propose a diffusion-bridge framework that characterizes the space of admissible solutions and restricts it via alignment constraints, treating paired supervision as an optional heuristic rather than a prerequisite. We validate our method on synthetic and real modality translation benchmarks across unpaired, semi-paired, and paired regimes, showing consistent performance across supervision levels. Notably, \textbf{it achieves near fully-paired quality with a substantial relaxation in pairing requirements, and remaining applicable in the unpaired regime}. These results highlight diffusion bridges as a flexible foundation for modality translation beyond fully paired data.