%2C%20a%20prediction%20algorithm%20that%20performs%20effective%20Bayesian%20inference%20by%20tightly%20coupling%20the%20top-down%20(prior)%20information%20with%20the%20bottom-up%20(data-driven)%20procedure%20via%20joint%20diffusion%20processes.%20We%20show%20the%20effectiveness%20of%20BDM%20on%20the%203D%20shape%20reconstruction%20task.%20Compared%20to%20prototypical%20deep%20learning%20data-driven%20approaches%20trained%20on%20paired%20(supervised)%20data-labels%20(e.g.%20image-point%20clouds)%20datasets%2C%20our%20BDM%20brings%20in%20rich%20prior%20information%20from%20standalone%20labels%20(e.g.%20point%20clouds)%20to%20improve%20the%20bottom-up%203D%20reconstruction.%20As%20opposed%20to%20the%20standard%20Bayesian%20frameworks%20where%20explicit%20prior%20and%20likelihood%20are%20required%20for%20the%20inference%2C%20BDM%20performs%20seamless%20information%20fusion%20via%20coupled%20diffusion%20processes%20with%20learned%20gradient%20computation%20networks.%20The%20specialty%20of%20our%20BDM%20lies%20in%20its%20capability%20to%20engage%20the%20active%20and%20effective%20information%20exchange%20and%20fusion%20of%20the%20top-down%20and%20bottom-up%20processes%20where%20each%20itself%20is%20a%20diffusion%20process.%20We%20demonstrate%20state-of-the-art%20results%20on%20both%20synthetic%20and%20real-world%20benchmarks%20for%203D%20shape%20reconstruction.)
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