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The design of biological sequences is essential for engineering functional biomolecules that contribute to advancements in human health and biotechnology. Recent advances in diffusion models, with their generative power and efficient conditional sampling, have made them a promising approach for sequence generation. To enhance model performance on limited data and enable multi-objective design and optimization, reinforcement learning (RL)-based fine-tuning has shown great potential. However, existing post-sampling and fine-tuning methods either lack stability in discrete optimization when avoiding gradients or incur high computational costs when employing gradient-based approaches, creating significant challenges for achieving both control and stability in the tuning process. To address these limitations, we propose GLID$^2$E, a gradient-free RL-based tuning approach for discrete diffusion models. Our method introduces a clipped likelihood constraint to regulate the exploration space and implements reward shaping to better align the generative process with design objectives, ensuring a more stable and efficient tuning process. By integrating these techniques, GLID$^2$E mitigates training instabilities commonly encountered in RL and diffusion-based frameworks, enabling robust optimization even in challenging biological design tasks. In the DNA sequence and protein sequence design systems, GLID$^2$E achieves competitive performance in function-based design while maintaining computational efficiency and a flexible tuning mechanism.