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 x0-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.
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→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.
Brownian Bridge Diffusion Models (BBDM) offer an appealing framework for image restoration and inverse problems by constructing a stochastic bridge from the clean signal directly to the degraded observation, rather than to pure noise. Despite their promise, the choice of bridge schedule is typically inherited from heuristics, and a principled analytical framework for schedule design has been lacking. In this work, we develop such a framework by offering a novel analysis of BBDM reverse dynamics under a Mixture-of-Gaussians (MoG) prior. This setting yields a closed-form ideal posterior and a corresponding MMSE denoiser, while the BBDM-induced reconstruction law is captured analytically through a tractable surrogate. Building on these expressions, we formulate two complementary schedule-design objectives: a Wasserstein criterion targeting perceptual quality and an MSE criterion targeting reconstruction fidelity. Our work exposes an inherent tradeoff between the two and proves the existence of universal schedules for both that are independent of the degradation and prior. Extensive experiments on controlled MoG settings confirm full alignment between theory and practice, and experiments on the FFHQ dataset across inpainting, deblurring, and super-resolution tasks validate the practical value of our schedule-design criteria.
Guidance methods, such as classifier-free guidance (CFG) and auto-guidance (AG), have advanced noise-to-data generation in diffusion models. Recently, bridge models have introduced a data-to-data generative process that can exploit an instructive clean prior. In this work, inspired by previous methods creating quality difference between denoising results as guidance, we propose a training-free bridge guidance method, termed Prior Guidance (PG). Specifically, we introduce a weak prior, which is unseen during bridge pre-training, hindering prior exploitation and thereby degrading denoising result. Then, we contrast it with the seen prior to highlight and enhance prior exploitation via a scaling factor. Moreover, we analyze the underlying mechanism of prior exploitation in the bridge process and design frequency-modulated prior guidance (FMPG), which tailors the guidance scale to low- and high-frequency bands coherent with bridge generative dynamics. To address prior exploitation in image in-painting, we develop a cascaded framework, CFG-FMPG, which first generates a noisy hidden representation via CFG and then exploits it as a generative prior with FMPG, fulfilling their complementary strengths without compromising inference efficiency. Experiments demonstrate that our PG methods consistently improve pre-trained bridge models across diverse image translation tasks.