Some oceanographic mixing parameterizations assume that transports depend nonlinearly on the buoyancy gradient; e.g., diffusivities are proportional to some power of the buoyancy gradient. In this paper we examine the consequences of these nonlinear-diffusion parameterizations by solving an initial value problem in which the t = 0 thermohaline fields are prepared as random and uncorrelated distributions of temperature and salinity. Solutions of the nonlinear diffusion equation as a ‘rundown’ problem show that correlations develop between the temperature and salinity. These correlations are such that the evolving thermohaline gradients tend to be strongly compensating in their joint effect on buoyancy.