Optimal Crystal Flow for Fast and Reliable Crystal Generation

$\text{De novo}$ crystal generation aims to discover novel materials by exploring the vast combinatorial space of atomic species and lattice geometries. While recent models based on diffusion and flow matching have shown strong generative capabilities, they often require a large number of sampling steps. More importantly, they struggle to generate reliable structures in out-of-distribution regimes, especially for systems larger than those seen during training. To address these limitations, we introduce $\text{Optimal Crystal Flow}$ (OCFlow), a flow matching framework that reduces unnecessarily long and curved coordinate paths by resolving $\text{intra-sample}$ ambiguity within each crystal. Experiments on the MP-20 and MPTS-52 benchmarks show that OCFlow is superior to or competitive with state-of-the-art baselines in sample validity and stability, with particularly strong performance on larger out-of-distribution systems while remaining effective with as few as ten network function evaluations. Together, these results show that per-structure optimal couplings provide both efficient sampling and robust generalization in crystal generation.