This paper presents a unified method for closed-form pricing of European options on assets with diffusion prices. The method uses linear and nonlinear time and scale changes to reduce complex diffusion processes to known processes, thereby generating option pricing formulas for new diffusion processes and unifying existing results. Applications include: systematically modelling the effects on option prices of time-dependent variability in the underlying asset price, valuing futures options and options on assets showing maturity-related or seasonal volatility, valuing options on new nonconstant elasticity-of-variance diffusion processes, and pricing generalized options.