# Joint Discrete-Continuous Flow Matching for Open-Vocabulary Inverse Design of Multilayer Optical Coatings

arXiv: https://arxiv.org/abs/2607.08392 · HTML: https://mlsanity.com/paper/2607.08392/

## 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 4 of its 61 references that are in the map.
- First posted on arXiv 9 Jul 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, 4 of 4)

- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Inverse Design of Optical Multilayer Thin Films using Robust Masked Diffusion Models](https://mlsanity.com/paper/2604.01106/) (2026)
- [PRISM: Position-encoded Regressive Inverse Spectral Model for Multilayer Thin-Film Design](https://mlsanity.com/paper/2605.26502/) (2026)

## Abstract (arXiv)

Optical multilayer coatings are used in imaging optics, lasers, telecommunications, solar cells, and radiative cooling, where the spectral response required by each application is achieved by a well-designed layer structure. However, existing design methods have limitations. Local methods refine a starting design efficiently but depend on its quality, and global searches require up to millions of transfer-matrix evaluations per target. Existing deep-learning inverse-design models are fast, but they are trained for a fixed set of materials and a fixed wavelength band, and they either optimize the thicknesses for a fixed material sequence or choose them from a discrete grid. In this paper, we present IrisFlow, a generative model that addresses these limitations by taking each candidate material as its optical constants and the target spectrum together with its wavelengths as input. It generates the material and the continuous thickness of every layer jointly, by coupled discrete and continuous flow matching in a single network. We demonstrate its performance through design with materials outside the training library and on bands beyond the training range, and through comparisons with classical optimizers and an existing deep-learning model. We also demonstrate its usability in a practical design workflow by designing four colored solar-reflective coatings with the calibrated optical constants of an existing deposition system. Combined with a local refinement of its ten best designs, it reduces the number of transfer-matrix evaluations about 500-fold relative to needle optimization at comparable accuracy. The code, trained model, and training and test data are publicly available.