# Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

arXiv: https://arxiv.org/abs/2302.12881 · HTML: https://mlsanity.com/paper/2302.12881/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 37 of its 60 references that are in the map.
- First posted on arXiv 24 Feb 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, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Video Pixel Networks](https://mlsanity.com/paper/1610.00527/) (2016)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscaling](https://mlsanity.com/paper/1812.01608/) (2018)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Distill-and-Compare: Auditing Black-Box Models Using Transparent Model Distillation](https://mlsanity.com/paper/1710.06169/) (2017)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)

## Built on by (most cited first, 24 of 24)

- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generation](https://mlsanity.com/paper/2502.01692/) (2025)
- [Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling](https://mlsanity.com/paper/2308.14035/) (2023)
- [Conditional score-based diffusion models for solving inverse problems in mechanics](https://mlsanity.com/paper/2406.13154/) (2024)
- [A Large Language Model and Denoising Diffusion Framework for Targeted Design of Microstructures with Commands in Natural Language](https://mlsanity.com/paper/2409.14473/) (2024)
- [Diffusion model based data generation for partial differential equations](https://mlsanity.com/paper/2306.11075/) (2023)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [Nonlinear Inverse Design of Mechanical Multi-Material Metamaterials Enabled by Video Denoising Diffusion and Structure Identifier](https://mlsanity.com/paper/2409.13908/) (2024)
- [MIND: Microstructure INverse Design with Generative Hybrid Neural Representation](https://mlsanity.com/paper/2502.02607/) (2025)
- [Synthesizing realistic sand assemblies with denoising diffusion in latent space](https://mlsanity.com/paper/2306.04411/) (2023)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [GrainPaint: A multi-scale diffusion-based generative model for microstructure reconstruction of large-scale objects](https://mlsanity.com/paper/2503.04776/) (2025)
- [Univariate Conditional Variational Autoencoder for Morphogenic Patterns Design in Frontal Polymerization-Based Manufacturing](https://mlsanity.com/paper/2410.17518/) (2024)
- [PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structure](https://mlsanity.com/paper/2506.11055/) (2025)
- [A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials](https://mlsanity.com/paper/2603.18225/) (2026)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [Denoising diffusion models for inverse design of inflatable structures with programmable deformations](https://mlsanity.com/paper/2508.13097/) (2025)
- [RAG: A Random-Forest-Based Generative Design Framework for Uncertainty-Aware Design of Metamaterials with Complex Functional Response Requirements](https://mlsanity.com/paper/2601.13233/) (2026)
- [PoreDiT: A Scalable Generative Model for Large-Scale Digital Rock Reconstruction](https://mlsanity.com/paper/2604.10171/) (2026)
- [Multiphase-Diff: Diffusion-Based Generative Modeling for High-Contrast Multiphase Physical Systems with Sharp Interfaces](https://mlsanity.com/paper/2608.13669/) (2026)
- [DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search](https://mlsanity.com/paper/2610.14999/) (2026)

## Abstract (arXiv)

In this paper, we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive responses. To identify the subset of microstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. The results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, the resulting algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. The algorithm is tested on the open-source mechanical MNIST data set. Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media but also learns the nonlinear structure-property map to quantitatively understand the multiscale interplay among the geometry and topology and their effective macroscopic properties.