We present parallel algorithms for processing, extracting and rendering adaptively sampled regular terrain datasets represented as a multiresolution model defined by a super-square-based diamond hierarchy. This model represents a terrain as a nested triangle mesh generated through a series of longest edge bisections and encoded in an implicit hierarchical structure, which clusters triangles into diamonds and diamonds into super-squares. We decompose the problem into three parallel algorithms for performing: generation of the diamond hierarchy from a regularly distributed terrain dataset, selective refinement on the diamond hierarchy and generation of the corresponding crack-free triangle mesh for processing and rendering. We avoid the data transfer bottleneck common to previous approaches by processing all data entirely on the GPU. We demonstrate that this parallel approach can be successfully applied to interactive terrain visualization with a high tessellation quality on commodity GPUs.