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.

Bayesian Diffusion Models (BDM)通过紧密地将自上而下的（先验）信息与自下而上的（数据驱动）过程通过联合扩散过程有效地进行贝叶斯推断，展现了在3D形状重建任务上的有效性。相较于典型的用于配对（监督）数据标签（例如图像点云）数据集训练的深度学习数据驱动方法，我们的BDM从单独的标签（例如点云）中引入丰富的先验信息，以改善自下而上的3D重建。与标准的贝叶斯框架要求显式的先验和似然不同，BDM通过学习到的梯度计算网络通过耦合扩散过程实现无缝信息融合。我们在合成和真实的3D形状重建基准测试中展示了最先进的结果。

贝叶斯扩散模型用于3D形状重建