The use of spatial high-order statistics has been previously proposed as an alternative to introduce richer information about complex spatial patterns in the simulation of continuous attributes. These statistics are normally inferred from exhaustive quasi -support training images. Spatial high-order statistics values are combined within series of orthogonal polynomials to approximate local conditional distributions that can be used for the drawing of simulated point-support values. This paper extends this formalism to direct block-support simulation. This is achieved by inferring block-point high-order statistics from up-scaled training images and incorporating these statistics in the orthogonal polynomials approximation of the conditional distributions. This methodology is computationally expensive, so a reasonable option is to approximate all the required local conditional distributions only once. These can be subsequently sampled by different fields of correlated probabilities to produce multiple realizations of the attribute. The resulting simulated maps reproduce the high-order statistics of the up-scaled training image and they also match the up-scaled global distribution of the attribute.