用多项式模拟掌纹，生成逼真且可调控差异的合成掌纹数据。

Palmprint recognition is significantly limited by the lack of large-scale publicly available datasets. Previous methods have adopted Bézier curves to simulate the palm creases, which then serve as input for conditional GANs to generate realistic palmprints. However, without employing real data fine-tuning, the performance of the recognition model trained on these synthetic datasets would drastically decline, indicating a large gap between generated and real palmprints. This is primarily due to the utilization of an inaccurate palm crease representation and challenges in balancing intra-class variation with identity consistency. To address this, we introduce a polynomial-based palm crease representation that provides a new palm crease generation mechanism more closely aligned with the real distribution. We also propose the palm creases conditioned diffusion model with a novel intra-class variation control method. By applying our proposed $K$-step noise-sharing sampling, we are able to synthesize palmprint datasets with large intra-class variation and high identity consistency. Experimental results show that, for the first time, recognition models trained solely on our synthetic datasets, without any fine-tuning, outperform those trained on real datasets. Furthermore, our approach achieves superior recognition performance as the number of generated identities increases.