FieldForge: A Pretraining and Post-Training Framework for Flow-Based Crystal Generation

Generating thermodynamically competitive crystals while retaining novelty remains a central challenge in materials discovery. To address this challenge, we present FieldForge, a flow-based training framework that unifies pretraining (PT), supervised fine-tuning (SFT), and reinforcement learning (RL) within a single crystal generator. Pretraining combines a Transformer supporting variable atom counts with flow matching, while respecting crystal geometry throughout the generative process. SFT then adapts the pretrained generative distribution through controlled data selection, preparing the generator for RL without introducing additional training structures. RL uses a GRPO-inspired critic-free policy update to refine the same velocity field using stability, novelty, and diversity rewards, with stability estimates provided by an interatomic potential. On the MP-20 track of LeMat-GenBench, the pretrained FieldForge model achieves state-of-the-art stable-unique-novel (SUN) and metastable-unique-novel (MSUN) rates, combining thermodynamic quality with uniqueness and novelty. SFT followed by RL further improves generation performance on both MP-20 and Alex-MP-20, demonstrating the effectiveness of the complete training framework.