  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.
