# Compositional Generative Inverse Design

arXiv: https://arxiv.org/abs/2401.13171 · HTML: https://mlsanity.com/paper/2401.13171/

## Key facts

- Cited by 20 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 25 of its 49 references that are in the map.
- First posted on arXiv 24 Jan 2024.

## 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)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Pre-Trained Language Models for Interactive Decision-Making](https://mlsanity.com/paper/2202.01771/) (2022)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems](https://mlsanity.com/paper/2307.08423/) (2023)
- [Compositional 3D Scene Generation using Locally Conditioned Diffusion](https://mlsanity.com/paper/2303.12218/) (2023)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Compositional Foundation Models for Hierarchical Planning](https://mlsanity.com/paper/2309.08587/) (2023)
- [Learning to Compose Visual Relations](https://mlsanity.com/paper/2111.09297/) (2021)
- [Controllable and Compositional Generation with Latent-Space Energy-Based Models](https://mlsanity.com/paper/2110.10873/) (2021)
- [Compositional Diffusion-Based Continuous Constraint Solvers](https://mlsanity.com/paper/2309.00966/) (2023)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [Model Based Planning with Energy Based Models](https://mlsanity.com/paper/1909.06878/) (2019)
- [Energy-based Models are Zero-Shot Planners for Compositional Scene Rearrangement](https://mlsanity.com/paper/2304.14391/) (2023)
- [Probabilistic Adaptation of Text-to-Video Models](https://mlsanity.com/paper/2306.01872/) (2023)
- [Benchmarking deep inverse models over time, and the neural-adjoint method](https://mlsanity.com/paper/2009.12919/) (2020)
- [Bidirectional Learning for Offline Model-based Biological Sequence Design](https://mlsanity.com/paper/2301.02931/) (2023)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Time](https://mlsanity.com/paper/2206.15049/) (2022)
- [Autoinverse: Uncertainty Aware Inversion of Neural Networks](https://mlsanity.com/paper/2208.13780/) (2022)
- [Identifiability of Product of Experts Models](https://mlsanity.com/paper/2310.09397/) (2023)

## Built on by (most cited first, 20 of 20)

- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [DiffPhyCon: A Generative Approach to Control Complex Physical Systems](https://mlsanity.com/paper/2407.06494/) (2024)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Mechanisms of Projective Composition of Diffusion Models](https://mlsanity.com/paper/2502.04549/) (2025)
- [CL-DiffPhyCon: Closed-loop Diffusion Control of Complex Physical Systems](https://mlsanity.com/paper/2408.03124/) (2024)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)
- [Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning](https://mlsanity.com/paper/2509.24332/) (2025)
- [Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows](https://mlsanity.com/paper/2603.21210/) (2026)
- [Geometry-Aware Neural Optimizer for Shape Optimization and Inversion](https://mlsanity.com/paper/2605.04474/) (2026)
- [Controllable Image Generation with Composed Parallel Token Prediction](https://mlsanity.com/paper/2405.06535/) (2024)
- [Generative Inverse Design with Abstention via Diagonal Flow Matching](https://mlsanity.com/paper/2603.15925/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Co-PiLOT: Constrained Physics-Informed Latent Optimization for Target-Driven Inverse Design](https://mlsanity.com/paper/2609.37875/) (2026)
- [Deep Generative Prior for First Order Inverse Optimization](https://mlsanity.com/paper/2504.20278/) (2025)
- [Minimizing Structural Vibrations via Guided Flow Matching Design Optimization](https://mlsanity.com/paper/2506.15263/) (2025)
- [Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates](https://mlsanity.com/paper/2508.13088/) (2025)
- [Controllable Image Generation with Composed Parallel Token Prediction](https://mlsanity.com/paper/2604.05730/) (2026)
- [Diffusion Domain Expansion: Learning to Coordinate Pre-trained Diffusion Models](https://mlsanity.com/paper/2605.23275/) (2026)

## Abstract (arXiv)

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.