# LithoGRPO: Fast Inverse Lithography via GRPO Reinforced Flow Matching

arXiv: https://arxiv.org/abs/2606.00228 · HTML: https://mlsanity.com/paper/2606.00228/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 30 of its 77 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [TempFlow-GRPO: When Timing Matters for GRPO in Flow Models](https://mlsanity.com/paper/2508.04324/) (2025)
- [BranchGRPO: Stable and Efficient GRPO with Structured Branching in Diffusion Models](https://mlsanity.com/paper/2509.06040/) (2025)
- [Coefficients-Preserving Sampling for Reinforcement Learning with Flow Matching](https://mlsanity.com/paper/2509.05952/) (2025)
- [GRPO-Guard: Mitigating Implicit Over-Optimization in Flow Matching via Regulated Clipping](https://mlsanity.com/paper/2510.22319/) (2025)
- [DAMO: Deep Agile Mask Optimization for Full Chip Scale](https://mlsanity.com/paper/2008.00806/) (2020)
- [Fine-Grained GRPO for Precise Preference Alignment in Flow Models](https://mlsanity.com/paper/2510.01982/) (2025)
- [DiverseGRPO: Mitigating Mode Collapse in Image Generation via Diversity-Aware GRPO](https://mlsanity.com/paper/2512.21514/) (2025)
- [GARDO: Reinforcing Diffusion Models without Reward Hacking](https://mlsanity.com/paper/2512.24138/) (2025)
- [Generic Lithography Modeling with Dual-band Optics-Inspired Neural Networks](https://mlsanity.com/paper/2203.08616/) (2022)
- [E-GRPO: High Entropy Steps Drive Effective Reinforcement Learning for Flow Models](https://mlsanity.com/paper/2601.00423/) (2026)
- [Large Scale Mask Optimization Via Convolutional Fourier Neural Operator and Litho-Guided Self Training](https://mlsanity.com/paper/2207.04056/) (2022)
- [Multi-GRPO: Multi-Group Advantage Estimation for Text-to-Image Generation with Tree-Based Trajectories and Multiple Rewards](https://mlsanity.com/paper/2512.00743/) (2025)
- [ILILT: Implicit Learning of Inverse Lithography Technologies](https://mlsanity.com/paper/2405.03574/) (2024)
- [Rectangular Partitions of a Rectilinear Polygon](https://mlsanity.com/paper/2111.01970/) (2021)
- [Unitho: A Unified Multi-Task Framework for Computational Lithography](https://mlsanity.com/paper/2511.10255/) (2025)
- [Pushing the Limits of Inverse Lithography with Generative Reinforcement Learning](https://mlsanity.com/paper/2602.19027/) (2026)

## Abstract (arXiv)

In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow-matching paradigm with GRPO-based reinforcement learning (RL) fine-tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization-based approaches, RL in LithoGRPO exploits the explicitly defined, physics-based reward function of ILT, enabling optimization under complex, process-aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130x speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state-of-the-art performance over both optimization-based and learning-based methods, while maintaining efficient mask generation.