用扩散模型从原子对分布函数重建纳米结构，加速且更稳定。
CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution function
- 基于条件先验的潜在扩散模型，提升逆问题求解效率。
- 利用拉普拉斯矩阵替代距离矩阵，增强结构恢复稳定性。
- 生成结果符合实验观测与物理规律，适合材料逆设计研究。
纳米结构逆问题有助于揭示纳米材料性质与结构的关系。本研究聚焦于从原子对分布函数（PDF）重构单金属纳米颗粒（MMNPs）模型体系，将其视为高度病态的条件生成任务。提出一种基于条件先验的潜在扩散模型（CbLDM），通过引入条件先验近似估计后验分布p(z|x)，在潜在空间实现高效生成。同时，采用拉普拉斯矩阵替代传统距离矩阵，显著提升结构恢复的稳定性。实验表明，该模型可生成与PDF观测一致、且具有物理意义的纳米结构，为后续更复杂的逆问题研究奠定基础。
原文摘要 · Abstract (English)
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.
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