Displaying a large number of lines within a limited amount of screen space is a task that is common to many different classes of visualization techniques such as time-series visualizations, parallel coordinates, link-node diagrams, and phase-space diagrams. This paper addresses the challenging problems of cluttering and overdraw inherent to such visualizations. We generate a 2x2 tensor field during line rasterization that encodes the distribution of line orientations through each image pixel. Anisotropic diffusion of a noise texture is then used to generate a dense, coherent visualization of line orientation. In order to represent features of different scales, we employ a multi-resolution representation of the tensor field. The resulting technique can easily be applied to a wide variety of line-based visualizations. We demonstrate this for parallel coordinates, a time-series visualization, and a phase-space diagram. Furthermore, we demonstrate how to integrate a focus+context approach by incorporating a second tensor field. Our approach achieves interactive rendering performance for large data sets containing millions of data items, due to its image-based nature and ease of implementation on GPUs. Simulation results from computational fluid dynamics are used to evaluate the performance and usefulness of the proposed method.