Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by modeling the posterior as a time-reversed diffusion from a simple Gaussian prior. However, DDVI's fixed unconditional starting distribution remains far from the complex true posterior, resulting in inefficient inference trajectories and slow convergence. In this work, we propose Diffusion Bridge Variational Inference (DBVI), a principled extension of DDVI that initiates the reverse diffusion from a learnable, data-dependent initial distribution. This initialization is parameterized via an amortized neural network and progressively adapted using gradients from the ELBO objective, reducing the posterior gap and improving sample efficiency. To enable scalable amortization, we design the network to operate on the inducing inputs, which serve as structured, low-dimensional summaries of the dataset and naturally align with the inducing variables' shape. DBVI retains the mathematical elegance of DDVI, including Girsanov-based ELBOs and reverse-time SDEs,while reinterpreting the prior via a Doob-bridged diffusion process. We derive a tractable training objective under this formulation and implement DBVI for scalable inference in large-scale DGPs. Across regression, classification, and image reconstruction tasks, DBVI consistently outperforms DDVI and other variational baselines in predictive accuracy, convergence speed, and posterior quality.

翻译：深度高斯过程（DGPs）能够实现表达力强的层次贝叶斯建模，但在后验推断（尤其是针对诱导变量）方面提出了重大挑战。去噪扩散变分推断（DDVI）通过将后验建模为从简单高斯先验出发的时间反向扩散来解决此问题。然而，DDVI固定的无条件起始分布与复杂的真实后验相距甚远，导致推断轨迹效率低下且收敛缓慢。本文提出扩散桥变分推断（DBVI），作为DDVI的原则性扩展方法，该方法从可学习的、数据依赖的初始分布启动反向扩散过程。该初始化通过摊销神经网络进行参数化，并利用ELBO目标的梯度逐步调整，从而减小后验差距并提升采样效率。为实现可扩展的摊销机制，我们设计网络使其在诱导输入上操作，这些输入作为数据集的结构化低维摘要，并自然地与诱导变量的形状对齐。DBVI保留了DDVI的数学优雅性（包括基于Girsanov定理的ELBO和反向时间SDE），同时通过Doob桥接扩散过程重新诠释了先验分布。我们在此框架下推导出可处理的训练目标，并实现了DBVI用于大规模DGPs的可扩展推断。在回归、分类和图像重建任务中，DBVI在预测精度、收敛速度和后验质量方面持续优于DDVI及其他变分基线方法。