Preserving intellectual property (IP) within a pre-trained diffusion model is critical for protecting the model's copyright and preventing unauthorized model deployment. In this regard, model watermarking is a common practice for IP protection that embeds traceable information within models and allows for further verification. Nevertheless, existing watermarking schemes often face challenges due to their vulnerability to fine-tuning, limiting their practical application in general pre-training and fine-tuning paradigms. Inspired by using mode connectivity to analyze model performance between a pair of connected models, we investigate watermark vulnerability by leveraging Linear Mode Connectivity (LMC) as a proxy to analyze the fine-tuning dynamics of watermark performance. Our results show that existing watermarked models tend to converge to sharp minima in the loss landscape, thus making them vulnerable to fine-tuning. To tackle this challenge, we propose RoMa, a Robust Model watermarking scheme that improves the robustness of watermarks against fine-tuning. Specifically, RoMa decomposes watermarking into two components, including Embedding Functionality, which preserves reliable watermark detection capability, and Path-specific Smoothness, which enhances the smoothness along the watermark-connected path to improve robustness. Extensive experiments on benchmark datasets MS-COCO-2017 and CUB-200-2011 demonstrate that RoMa significantly improves watermark robustness against fine-tuning while maintaining generation quality, outperforming baselines. The code is available at https://github.com/xiekks/RoMa.