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

Bayesian Diffusion Models for 3D Shape Reconstruction

We introduce generative models for accelerating simulations of complex
systems through learning and evolving their effective dynamics. In the proposed
Generative Learning of Effective Dynamics (G-LED), instances of high
dimensional data are down sampled to a lower dimensional manifold that is
evolved through an auto-regressive attention mechanism. In turn, Bayesian
diffusion models, that map this low-dimensional manifold onto its corresponding
high-dimensional space, capture the statistics of the system dynamics. We
demonstrate the capabilities and drawbacks of G-LED in simulations of several
benchmark systems, including the Kuramoto-Sivashinsky (KS) equation,
two-dimensional high Reynolds number flow over a backward-facing step, and
simulations of three-dimensional turbulent channel flow. The results
demonstrate that generative learning offers new frontiers for the accurate
forecasting of the statistical properties of complex systems at a reduced
computational cost.

通过学习和演变系统的有效动力学，我们引入生成模型来加速复杂系统的模拟。在提出的 G-LED 中，高维数据的实例被降采样到一个更低维度的流形中，并通过自回归注意机制进行演变。反过来，贝叶斯扩散模型将这个低维流形映射到相应的高维空间，捕捉系统动力学的统计特性。我们在几个基准系统的模拟中展示了 G-LED 的能力和局限性，包括 Kuramoto-Sivashinsky（KS）方程、反向阶梯上的二维高雷诺数流动和三维湍流通道流的模拟。结果表明，生成学习为以更低的计算成本准确预测复杂系统的统计特性开辟了新的前沿。