# Inverse Design of Metamaterials with Manufacturing-Guiding Spectrum-to-Structure Conditional Diffusion Model

arXiv: https://arxiv.org/abs/2506.07083 · HTML: https://mlsanity.com/paper/2506.07083/

## Key facts

- Cited by 2 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 22 of its 70 references that are in the map.
- First posted on arXiv 8 Jun 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, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [Rethinking the Spatial Inconsistency in Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2404.05384/) (2024)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [A Generative Model for Inverse Design of Metamaterials](https://mlsanity.com/paper/1805.10181/) (2018)
- [Freeform Diffractive Metagrating Design Based on Generative Adversarial Networks](https://mlsanity.com/paper/1811.12436/) (2018)
- [Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures](https://mlsanity.com/paper/1902.03865/) (2019)
- [VAE Approximation Error: ELBO and Exponential Families](https://mlsanity.com/paper/2102.09310/) (2021)
- [Bayesian optimization with known experimental and design constraints for chemistry applications](https://mlsanity.com/paper/2203.17241/) (2022)
- [Diffusion Probabilistic Model Based Accurate and High-Degree-of-Freedom Metasurface Inverse Design](https://mlsanity.com/paper/2304.13038/) (2023)

## Built on by (most cited first, 2 of 2)

- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)

## Abstract (arXiv)

Metamaterials are artificially engineered structures that manipulate electromagnetic waves, having optical properties absent in natural materials. Recently, machine learning for the inverse design of metamaterials has drawn attention. However, the highly nonlinear relationship between the metamaterial structures and optical behaviour, coupled with fabrication difficulties, poses challenges for using machine learning to design and manufacture complex metamaterials. Herein, we propose a general framework that implements customised spectrum-to-shape and size parameters to address one-to-many metamaterial inverse design problems using conditional diffusion models. Our method exhibits superior spectral prediction accuracy, generates a diverse range of patterns compared to other typical generative models, and offers valuable prior knowledge for manufacturing through the subsequent analysis of the diverse generated results, thereby facilitating the experimental fabrication of metamaterial designs. We demonstrate the efficacy of the proposed method by successfully designing and fabricating a free-form metamaterial with a tailored selective emission spectrum for thermal camouflage applications.