The Diamond-Square Algorithm is an improvement on the Midpoint Displacement Algorithm which reduces the visual artifacts of that algorithm by including an intermediate step which considers diamond shaped squares. It is also known as the random midpoint displacement fractal, the cloud fractal or the plasma fractal.
Eventhough it is an improvement on midpoint displacement, the generated terrain still suffers from axis aligned ridges and is considered flawed by the authors.
PCG Wiki References
Diamond-Square Algorithm - Wikipedia article on the Diamond-Square Algorithm.