Diffusion priors for Bayesian 3D reconstruction from incomplete measurements

TL;DR

This paper introduces a Bayesian 3D reconstruction method using diffusion models as priors, enabling effective recovery of complex structures from incomplete and noisy data, especially in cryo-EM applications.

Contribution

It proposes integrating diffusion models as priors within a Bayesian framework for 3D reconstruction from sparse measurements, advancing beyond traditional generic priors.

Findings

Successful 3D reconstruction from sparse cryo-EM data

Diffusion priors improve reconstruction quality with limited data

Applicable to biomolecular and household object models

Abstract

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.