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Description: In siliciclastic and carbonate reservoirs, depositional facies are often described as being organized in cyclic successions that are overprinted by diagenesis. Most reservoir modelling workflows are not able to reproduce stochastically such patterns. Herein, a novel geostatistical method is developed to model depositional facies architectures that are rhythmic and cyclic, together with superimposed diagenetic facies. The method uses truncated Pluri-Gaussian random functions constrained by transiograms. Cyclicity is defined as an asymmetric ordering between facies, and its direction is given by a three-dimensional vector, called shift. This method is illustrated on two case studies. Outcrop data of the Triassic Latemar carbonate platform, northern Italy, are used to model shallowing-upward facies cycles in the vertical direction. A satellite image of the modern Bermuda platform interior is used to model facies cycles in the windward-to-leeward lateral direction. As depositional facies architectures are modelled using two Gaussian random functions, a third Gaussian random function is added to model diagenesis. Thereby, depositional and diagenetic facies can exhibit spatial asymmetric relations. The method is applied in two regions of the Latemar carbonate platform that experience two different types of diagenetic transformation: syn-depositional dolomite formation, and post-depositional fracture-related diagenesis. The method can also incorporate proportion curves to model non-stationary facies proportions. This is illustrated in Cretaceous shallow-marine sandstones and mudstones, Book Cliffs, Utah, for which cyclic facies and diagenetic patterns are constrained by embedded transition probabilities.