CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution function

The nanostructure inverse problem is an attractive problem that helps researchers to understand the relationship between the properties and the structure of nanomaterials. This study focuses on the problem of recovering the model system of monometallic nanoparticles (MMNPs) from their pair distribution function (PDF) and regards it as a highly ill-posed conditional generation task. This study proposes a Condition-based Latent Diffusion Model (CbLDM) as a feasible solution to this problem. This model demonstrates an acceleration approach within the framework of a latent diffusion model by using conditional priors to estimate the conditional posterior distribution, which is an approximate distribution of p(z|x). In addition, this study uses Laplacian matrix instead of distance matrix to recover the nanostructure, which helps to improve stability. Our study demonstrates that a latent diffusion model with a conditional prior can generate nanostructures that are consistent with PDF observations and physically meaningful, thereby laying the groundwork for subsequent more complex inverse problems.