This paper introduces Diversity-Driven RandomWalks (D-RDW), a lightweight algorithm and re-ranking technique that generates diverse news recommendations. D-RDW is a societal recommender, which combines the diversification capabilities of the traditional random walk algorithms with customizable target distributions of news article properties. In doing so, our model provides a transparent approach for editors to incorporate norms and values into the recommendation process. D-RDW shows enhanced performance across key diversity metrics that consider the articles' sentiment and political party mentions when compared to state-of-the-art neural models. Furthermore, D-RDW proves to be more computationally efficient than existing approaches.