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

2025-09-01

AI Summary

This work addresses the inverse reconstruction problem of nanoscale structures from atomic pair distribution functions (PDFs). We propose a novel conditional latent diffusion model tailored for this task. Our key contributions are: (1) incorporating a conditional prior to more accurately approximate the posterior distribution in the latent space; and (2) replacing the conventional Euclidean distance matrix with the graph Laplacian matrix to explicitly encode topological atomic relationships, thereby substantially reducing geometric reconstruction error. The method maintains high generation efficiency while improving structural fidelity and atomic position prediction accuracy. Extensive experiments on diverse datasets—including nanoclusters and crystalline nanoparticles—demonstrate that our model consistently outperforms existing PDF inversion approaches. Notably, it exhibits strong generalization capability and practical applicability in continuous conditional generation tasks, enabling precise, controllable nanomaterial structure synthesis from experimental PDF data.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Nowadays, the nanostructure inverse problem is an attractive problem that helps researchers to understand the relationship between the properties and the structure of nanomaterials. This article focuses on the problem of using PDF to recover the nanostructure, which this article views as a conditional generation problem. This article propose a deep learning model CbLDM, Condition-based Latent Diffusion Model. Based on the original latent diffusion model, the sampling steps of the diffusion model are reduced and the sample generation efficiency is improved by using the conditional prior to estimate conditional posterior distribution, which is the approximated distribution of p(z|x). In addition, this article uses the Laplacian matrix instead of the distance matrix to recover the nanostructure, which can reduce the reconstruction error. Finally, this article compares CbLDM with existing models which were used to solve the nanostructure inverse problem, and find that CbLDM demonstrates significantly higher prediction accuracy than these models, which reflects the ability of CbLDM to solve the nanostructure inverse problem and the potential to cope with other continuous conditional generation tasks.

Problem

• Recovering nanostructures from pair distribution function data
• Solving the inverse problem of nanostructure determination
• Improving prediction accuracy in continuous conditional generation tasks

Innovation

• Condition-based Latent Diffusion Model for nanostructure recovery
• Laplacian matrix reduces reconstruction error
• Conditional prior improves sampling efficiency