In this paper we show that simple noise regularisation can be an effective way to address GNN oversmoothing. First we argue that regularisers addressing oversmoothing should both penalise node latent similarity and encourage meaningful node representations. From this observation we derive "Noisy Nodes", a simple technique in which we corrupt the input graph with noise, and add a noise correcting node-level loss. The diverse node level loss encourages latent node diversity, and the denoising objective encourages graph manifold learning. Our regulariser applies well-studied methods in simple, straightforward ways which allow even generic architectures to overcome oversmoothing and achieve state of the art results on quantum chemistry tasks, and improve results significantly on Open Graph Benchmark (OGB) datasets. Our results suggest Noisy Nodes can serve as a complementary building block in the GNN toolkit.