# Denoising diffusion models for inverse design of inflatable structures with programmable deformations

arXiv: https://arxiv.org/abs/2508.13097 · HTML: https://mlsanity.com/paper/2508.13097/

## 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 14 of its 79 references that are in the map.
- First posted on arXiv 18 Aug 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, 14 of 14)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Diffusion Model as Representation Learner](https://mlsanity.com/paper/2308.10916/) (2023)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Balancing reconstruction error and Kullback-Leibler divergence in Variational Autoencoders](https://mlsanity.com/paper/2002.07514/) (2020)
- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [Probing the Limits and Capabilities of Diffusion Models for the Anatomic Editing of Digital Twins](https://mlsanity.com/paper/2401.00247/) (2023)
- [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)
- [Synthesizing realistic sand assemblies with denoising diffusion in latent space](https://mlsanity.com/paper/2306.04411/) (2023)

## Abstract (arXiv)

Programmable structures are systems whose undeformed geometries and material property distributions are deliberately designed to achieve prescribed deformed configurations under specific loading conditions. Inflatable structures are a prominent example, using internal pressurization to realize large, nonlinear deformations in applications ranging from soft robotics and deployable aerospace systems to biomedical devices and adaptive architecture. We present a generative design framework based on denoising diffusion probabilistic models (DDPMs) for the inverse design of elastic structures undergoing large, nonlinear deformations under pressure-driven actuation. The method formulates the inverse design as a conditional generation task, using geometric descriptors of target deformed states as inputs and outputting image-based representations of the undeformed configuration. Representing these configurations as simple images is achieved by establishing a pre- and postprocessing pipeline that involves a fixed image processing, simulation setup, and descriptor extraction methods. Numerical experiments with scalar and higher-dimensional descriptors show that the framework can quickly produce diverse undeformed configurations that achieve the desired deformations when inflated, enabling parallel exploration of viable design candidates while accommodating complex constraints.