Diffusion models have demonstrated remarkable potential in generating high-quality images. However, their tendency to replicate training data raises serious privacy concerns, particularly when the training datasets contain sensitive or private information. Existing mitigation strategies primarily focus on reducing image duplication, modifying the cross-attention mechanism, and altering the denoising backbone architecture of diffusion models. Moreover, recent work has shown that adding a consistent small amount of noise to text embeddings can reduce replication to some degree. In this work, we begin by analyzing the impact of adding varying amounts of noise. Based on our analysis, we propose a fine-grained noise injection technique that probabilistically adds a larger amount of noise to token embeddings. We refer to our method as Fine-grained Probabilistic Addition of Noise (FPAN). Through our extensive experiments, we show that our proposed FPAN can reduce replication by an average of 28.78% compared to the baseline diffusion model without significantly impacting image quality, and outperforms the prior consistent-magnitude-noise-addition approach by 26.51%. Moreover, when combined with other existing mitigation methods, our FPAN approach can further reduce replication by up to 16.82% with similar, if not improved, image quality.