Diffusion-Based Symbolic Regression

Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic regression. We construct a random mask-based diffusion and denoising process to generate diverse and high-quality equations. We integrate this generative processes with a token-wise Group Relative Policy Optimization (GRPO) method to conduct efficient reinforcement learning on the given measurement dataset. In addition, we introduce a long short-term risk-seeking policy to expand the pool of top-performing candidates, further enhancing performance. Extensive experiments and ablation studies have demonstrated the effectiveness of our approach.

@article{bastiani2025_2505.24776,
  title={ Diffusion-Based Symbolic Regression },
  author={ Zachary Bastiani and Robert M. Kirby and Jacob Hochhalter and Shandian Zhe },
  journal={arXiv preprint arXiv:2505.24776},
  year={ 2025 }
}