We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We show the effectiveness of BDM on the 3D shape reconstruction task. Compared to prototypical deep learning data-driven approaches trained on paired (supervised) data-labels (e.g. image-point clouds) datasets, our BDM brings in rich prior information from standalone labels (e.g. point clouds) to improve the bottom-up 3D reconstruction. As opposed to the standard Bayesian frameworks where explicit prior and likelihood are required for the inference, BDM performs seamless information fusion via coupled diffusion processes with learned gradient computation networks. The specialty of our BDM lies in its capability to engage the active and effective information exchange and fusion of the top-down and bottom-up processes where each itself is a diffusion process. We demonstrate state-of-the-art results on both synthetic and real-world benchmarks for 3D shape reconstruction.

翻译：我们提出贝叶斯扩散模型（BDM），这是一种通过联合扩散过程紧密耦合自上而下（先验）信息与自下而上（数据驱动）流程，从而执行高效贝叶斯推理的预测算法。我们在三维形状重建任务上验证了BDM的有效性。与在配对（监督）数据标签（如图像-点云）数据集上训练的典型深度学习数据驱动方法相比，我们的BDM利用来自独立标签（如点云）的丰富先验信息来改进自下而上的三维重建。与需要显式先验和似然进行推理的标准贝叶斯框架不同，BDM通过带有学习梯度计算网络的耦合扩散过程实现无缝信息融合。BDM的特殊之处在于其能够促使自上而下与自下而上流程（每个流程本身即为扩散过程）进行主动且高效的信息交换与融合。我们在三维形状重建的合成数据集和真实世界基准测试上均展示了最先进的性能。