# Inverse design with conditional cascaded diffusion models

arXiv: https://arxiv.org/abs/2408.08526 · HTML: https://mlsanity.com/paper/2408.08526/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 16 Aug 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [Accelerating Score-based Generative Models with Preconditioned Diffusion Sampling](https://mlsanity.com/paper/2207.02196/) (2022)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [Diffusing the Optimal Topology: A Generative Optimization Approach](https://mlsanity.com/paper/2303.09760/) (2023)

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

- [Agentic Large Language Models for Conceptual Systems Engineering and Design](https://mlsanity.com/paper/2507.08619/) (2025)
- [Conditional Flow Matching for ML-Based Inverse Design Problems](https://mlsanity.com/paper/2609.00863/) (2026)

## Abstract (arXiv)

Adjoint-based design optimizations are usually computationally expensive and those costs scale with resolution. To address this, researchers have proposed machine learning approaches for inverse design that can predict higher-resolution solutions from lower cost/resolution ones. Due to the recent success of diffusion models over traditional generative models, we extend the use of diffusion models for multi-resolution tasks by proposing the conditional cascaded diffusion model (cCDM). Compared to GANs, cCDM is more stable to train, and each diffusion model within the cCDM can be trained independently, thus each model's parameters can be tuned separately to maximize the performance of the pipeline. Our study compares cCDM against a cGAN model with transfer learning. Our results demonstrate that the cCDM excels in capturing finer details, preserving volume fraction constraints, and minimizing compliance errors in multi-resolution tasks when a sufficient amount of high-resolution training data (more than 102 designs) is available. Furthermore, we explore the impact of training data size on the performance of both models. While both models show decreased performance with reduced high-resolution training data, the cCDM loses its superiority to the cGAN model with transfer learning when training data is limited (less than 102), and we show the break-even point for this transition. Also, we highlight that while the diffusion model may achieve better pixel-wise performance in both low-resolution and high-resolution scenarios, this does not necessarily guarantee that the model produces optimal compliance error or constraint satisfaction.