Diffusion models have demonstrated significant potential in image generation. However, their ability to replicate training data presents a privacy risk, particularly when the training data includes confidential information. Existing mitigation strategies primarily focus on augmenting the training dataset, leaving the impact of diffusion model architecture under explored. In this paper, we address this gap by examining and mitigating the impact of the model structure, specifically the skip connections in the diffusion model's U-Net model. We first present our observation on a trade-off in the skip connections. While they enhance image generation quality, they also reinforce the memorization of training data, increasing the risk of replication. To address this, we propose a replication-aware U-Net (RAU-Net) architecture that incorporates information transfer blocks into skip connections that are less essential for image quality. Recognizing the potential impact of RAU-Net on generation quality, we further investigate and identify specific timesteps during which the impact on memorization is most pronounced. By applying RAU-Net selectively at these critical timesteps, we couple our novel diffusion model with a targeted training and inference strategy, forming a framework we refer to as LoyalDiffusion. Extensive experiments demonstrate that LoyalDiffusion outperforms the state-of-the-art replication mitigation method achieving a 48.63% reduction in replication while maintaining comparable image quality.