# Co-PiLOT: Constrained Physics-Informed Latent Optimization for Target-Driven Inverse Design

arXiv: https://arxiv.org/abs/2609.37875 · HTML: https://mlsanity.com/paper/2609.37875/

## Key facts

- Cited by 1 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 31 of its 67 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## 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 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Feedback Efficient Online Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2402.16359/) (2024)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [Towards Understanding the Mechanisms of Classifier-Free Guidance](https://mlsanity.com/paper/2505.19210/) (2025)
- [DeepAdjoint: An All-in-One Photonic Inverse Design Framework Integrating Data-Driven Machine Learning with Optimization Algorithms](https://mlsanity.com/paper/2209.15434/) (2022)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)

## Built on by (most cited first, 1 of 1)

- [Which alloy composition,what process parameters? Inferring the recipe from optimized metallic microstructure and texture](https://mlsanity.com/paper/2610.08165/) (2026)

## Abstract (arXiv)

Inverse design of physical systems (molecules, devices, microstructures) often reduces to optimizing a high-dimensional structure against an expensive black-box simulator. Direct search is difficult because the space is non-Euclidean, feasibility is hard to encode, and each evaluation is expensive. We present Co-PiLOT, a latent optimization approach that maps candidates through a generative encoder-decoder, uses the decoder as a learned validity prior, and searches the latent space with physics-informed black-box optimization. The framework is applied on the inverse design of magnesium alloy microstructure/texture. We develop a vision transformer based-encoder; paired with latent diffusion, diffusion transformer and rectified-flow transformer-based decoders on ~80,000 EBSD-derived microstructure dataset to learn a minimal bottleneck, z. The ViT-FMDiT model (z=768) reconstructs high-fidelity microstructure images (FID 27.86, MS-SSIM 0.178), which our self-segmenting orientation codec converts into input grids for crystal plasticity solver. Finally, we introduce MERIDIAN, an active latent optimizer driven by deep-kernel Gaussian-process uncertainty, failure-aware feasibility prediction, manifold-aware trust regions, and target-aware acquisition. Within a budget of 160 simulations, the ViT-FMDiT and MERIDIAN combination yields the best target-driven objective score, reducing the relative target error by 3--22% against seven baselines (DANTE, TuRBO, BAxUS, CMA-ES, DDOM, SEIKO, DDPO) on the same decoder.