Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the model such as sparsity, non-negativity or smoothness. However, in case of complex structured models such as images, graphs or three-dimensional (3D) objects,generic prior distributions tend to favor models that differ largely from those observed in the real world. Here we explore the use of diffusion models as priors that are combined with experimental data within a Bayesian framework. We use 3D point clouds to represent 3D objects such as household items or biomolecular complexes formed from proteins and nucleic acids. We train diffusion models that generate coarse-grained 3D structures at a medium resolution and integrate these with incomplete and noisy experimental data. To demonstrate the power of our approach, we focus on the reconstruction of biomolecular assemblies from cryo-electron microscopy (cryo-EM) images, which is an important inverse problem in structural biology. We find that posterior sampling with diffusion model priors allows for 3D reconstruction from very sparse, low-resolution and partial observations.

翻译：许多逆问题具有不适定性，需要借助先验信息来限制可接受模型的范围。贝叶斯方法将此类信息编码为施加于模型的先验分布，这些分布要求模型具备稀疏性、非负性或平滑性等通用特性。然而，对于图像、图或三维物体这类复杂结构化模型，通用先验分布往往倾向于生成与现实世界观测结果差异较大的模型。本研究探索在贝叶斯框架下，将扩散模型作为先验信息与实验数据相结合的方法。我们采用三维点云来表示三维物体（如家居物品）或由蛋白质与核酸构成的生物分子复合体。我们训练了能够生成中等分辨率粗粒度三维结构的扩散模型，并将其与不完整且含噪声的实验数据进行融合。为验证本方法的有效性，我们聚焦于冷冻电镜图像中生物分子组装体的重建问题——这是结构生物学领域一个重要的逆问题。研究发现，采用扩散模型先验进行后验采样，能够从极其稀疏、低分辨率且不完整的观测数据中实现三维重建。