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

arXiv: https://arxiv.org/abs/2509.01370 · HTML: https://mlsanity.com/paper/2509.01370/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 17 of its 82 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 17 of 17)

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- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
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- [UNIT-DDPM: UNpaired Image Translation with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.05358/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Dual Contradistinctive Generative Autoencoder](https://mlsanity.com/paper/2011.10063/) (2020)
- [From optimal transport to generative modeling: the VEGAN cookbook](https://mlsanity.com/paper/1705.07642/) (2017)
- [Deep K-SVD Denoising](https://mlsanity.com/paper/1909.13164/) (2019)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)

## Abstract (arXiv)

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.