Before revision:  Our approach is based on  the so-called diffusion canonical transformation method that allows us to uncover new multiparameter diffusions that are mapped onto various simpler underlying diffusions.
After revision:  Our approach is based on the so-called diffusion canonical transformation method that combines smooth monotonic mappings and measure changes via Doob-h transforms. This gives rise to new multi-parameter solvable diffusions that are mapped onto various simpler underlying diffusions.