Inverting real images into the noise space is essential for editing tasks using diffusion models, yet existing methods produce non-Gaussian noise with poor editability due to the inaccuracy in early noising steps. We identify the root cause: a mathematical singularity that renders inversion fundamentally ill-posed. We propose Singularity Skipping Inversion of Diffusion Models (SSI-DM), which bypasses this singular region by adding small noise before standard inversion. This simple approach produces inverted noise with natural Gaussian properties while maintaining reconstruction fidelity. As a plug-and-play technique compatible with general diffusion models, our method achieves superior performance on public image datasets for reconstruction and interpolation tasks, providing a principled and efficient solution to diffusion model inversion.