Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs require a computationally intensive sampling process that involves the simulation of a (stochastic) differential equation through hundreds of network evaluations. In this work, we take the first step in fast sampling of DDBMs without extra training, motivated by the well-established recipes in diffusion models. We generalize DDBMs via a class of non-Markovian diffusion bridges defined on the discretized timesteps concerning sampling, which share the same marginal distributions and training objectives, give rise to generative processes ranging from stochastic to deterministic, and result in diffusion bridge implicit models (DBIMs). DBIMs are not only up to 25$\times$ faster than the vanilla sampler of DDBMs but also induce a novel, simple, and insightful form of ordinary differential equation (ODE) which inspires high-order numerical solvers. Moreover, DBIMs maintain the generation diversity in a distinguished way, by using a booting noise in the initial sampling step, which enables faithful encoding, reconstruction, and semantic interpolation in image translation tasks. Code is available at \url{https://github.com/thu-ml/DiffusionBridge}.

翻译：去噪扩散桥模型（DDBMs）是扩散模型的一个强大变体，用于在任意给定的两个配对端点分布之间进行插值。尽管在图像翻译等任务中表现出色，DDBMs需要计算密集的采样过程，该过程涉及通过数百次网络评估来模拟（随机）微分方程。在本工作中，我们借鉴扩散模型中成熟的方案，首次在不进行额外训练的情况下实现了DDBMs的快速采样。我们通过一类定义在离散化采样时间步上的非马尔可夫扩散桥来推广DDBMs，这些扩散桥共享相同的边缘分布和训练目标，能够产生从随机到确定性的生成过程，并最终形成扩散桥隐式模型（DBIMs）。DBIMs不仅比DDBMs的原始采样器快达25倍，还导出了一个新颖、简洁且富有启发性的常微分方程（ODE）形式，这启发了高阶数值求解器的设计。此外，DBIMs通过在初始采样步骤中使用引导噪声，以一种独特的方式保持了生成多样性，从而在图像翻译任务中实现了忠实的编码、重建和语义插值。代码可在 \url{https://github.com/thu-ml/DiffusionBridge} 获取。