Graph-based collaborative filtering (CF) has emerged as a promising approach in recommender systems. Despite its achievements, graph-based CF models face challenges due to data sparsity and negative sampling. In this paper, we propose a novel Stochastic sampling for i) COntrastive views and ii) hard NEgative samples (SCONE) to overcome these issues. SCONE generates dynamic augmented views and diverse hard negative samples via a unified stochastic sampling approach based on score-based generative models. Our extensive experiments on 6 benchmark datasets show that SCONE consistently outperforms state-of-the-art baselines. SCONE shows efficacy in addressing user sparsity and item popularity issues, while enhancing performance for both cold-start users and long-tail items. Furthermore, our approach improves the diversity of the recommendation and the uniformity of the representations. The code is available at https://github.com/jeongwhanchoi/SCONE.