Recently, reinforcement learning (RL) has been employed for improving generative image super-resolution (ISR) performance. However, the current efforts are focused on multi-step generative ISR, while one-step generative ISR remains underexplored due to its limited stochasticity. In addition, RL methods such as Direct Preference Optimization (DPO) require the generation of positive and negative sample pairs offline, leading to a limited number of samples, while Group Relative Policy Optimization (GRPO) only calculates the likelihood of the entire image, ignoring local details that are crucial for ISR. In this paper, we propose Group Direct Preference Optimization (GDPO), a novel approach to integrate RL into one-step generative ISR model training. First, we introduce a noise-aware one-step diffusion model that can generate diverse ISR outputs. To prevent performance degradation caused by noise injection, we introduce an unequal-timestep strategy to decouple the timestep of noise addition from that of diffusion. We then present the GDPO strategy, which integrates the principle of GRPO into DPO, to calculate the group-relative advantage of each online generated sample for model optimization. Meanwhile, an attribute-aware reward function is designed to dynamically evaluate the score of each sample based on its statistics of smooth and texture areas. Experiments demonstrate the effectiveness of GDPO in enhancing the performance of one-step generative ISR models. Code: https://github.com/Joyies/GDPO.