Diffusion models have demonstrated promising performance in graph generation, significantly advancing related fields such as drug discovery. However, existing models face the challenge of data memorization, involving generating samples identical or highly similar to the training data, which limits their exploratory capabilities. This paper presents Random GCN Gradient Guidance (RG3), a training-free and plug-and-play approach that leverages GCN with random weights and incorporates a well-designed sampling strategy to address this issue in one denoising step. Experimental results across benchmark datasets demonstrate that RG3 effectively mitigates the problem of data memorization without compromising generation quality.