Recent advances in 3D Gaussian Splatting (3DGS) have achieved remarkable success in high-fidelity Novel View Synthesis (NVS), yet the optimization process inevitably introduces noisy Gaussian primitives due to the sparse and incomplete initialization from Structure-from-Motion (SfM) point clouds. Most existing methods focus solely on adjusting the positions of primitives during optimization, while neglecting the underlying spatial structure. To this end, we introduce a new perspective by formulating the optimization of 3DGS as a primitive denoising process and propose Denoising-GS, a spatial-aware denoising framework for Gaussian primitives by taking both the positions and spatial structure into consideration. Specifically, we design an optimizer that preserves the spatial optimization flow of primitives, facilitating coherent and directed denoising rather than random perturbations. Building upon this, the Spatial Gradient-based Denoising strategy jointly considers the spatial supports of primitives to ensure gradient-consistent updates. Furthermore, the Uncertainty-based Denoising module estimates primitive-wise uncertainty to prune redundant or noisy primitives, while the Spatial Coherence Refinement strategy selectively splits primitives in sparse regions to maintain structural completeness. Experiments conducted on three benchmark datasets demonstrate that Denoising-GS consistently enhances NVS fidelity while maintaining representation compactness, achieving state-of-the-art performance across all benchmarks. Source code and models will be made publicly available.