# Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographs

arXiv: https://arxiv.org/abs/2312.07832 · HTML: https://mlsanity.com/paper/2312.07832/

## 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 25 of its 73 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## 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, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusion](https://mlsanity.com/paper/2203.12621/) (2022)
- [Towards Deeper Understanding of Variational Autoencoding Models](https://mlsanity.com/paper/1702.08658/) (2017)
- [Stochastic Image Denoising by Sampling from the Posterior Distribution](https://mlsanity.com/paper/2101.09552/) (2021)
- [Generating 3D structures from a 2D slice with GAN-based dimensionality expansion](https://mlsanity.com/paper/2102.07708/) (2021)
- [A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions](https://mlsanity.com/paper/1805.02784/) (2018)
- [Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design](https://mlsanity.com/paper/1612.07401/) (2016)
- [Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics](https://mlsanity.com/paper/2206.01693/) (2022)
- [Microstructure synthesis using style-based generative adversarial network](https://mlsanity.com/paper/1909.07042/) (2019)
- [Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling](https://mlsanity.com/paper/2308.14035/) (2023)

## Abstract (arXiv)

Integrated computational materials engineering (ICME) has significantly enhanced the systemic analysis of the relationship between microstructure and material properties, paving the way for the development of high-performance materials. However, analyzing microstructure-sensitive material behavior remains challenging due to the scarcity of three-dimensional (3D) microstructure datasets. Moreover, this challenge is amplified if the microstructure is anisotropic, as this results in anisotropic material properties as well. In this paper, we present a framework for reconstruction of anisotropic microstructures solely based on two-dimensional (2D) micrographs using conditional diffusion-based generative models (DGMs). The proposed framework involves spatial connection of multiple 2D conditional DGMs, each trained to generate 2D microstructure samples for three different orthogonal planes. The connected multiple reverse diffusion processes then enable effective modeling of a Markov chain for transforming noise into a 3D microstructure sample. Furthermore, a modified harmonized sampling is employed to enhance the sample quality while preserving the spatial connection between the slices of anisotropic microstructure samples in 3D space. To validate the proposed framework, the 2D-to-3D reconstructed anisotropic microstructure samples are evaluated in terms of both the spatial correlation function and the physical material behavior. The results demonstrate that the framework is capable of reproducing not only the statistical distribution of material phases but also the material properties in 3D space. This highlights the potential application of the proposed 2D-to-3D reconstruction framework in establishing microstructure-property linkages, which could aid high-throughput material design for future studies