This paper presents a comprehensive Bayesian refinement of the chronology of Tiwanaku material culture. To place this material pattern in space, we present a presence-only map of most sites with Tiwanaku redware ceramics, snuff trays, and textiles. We compile radiocarbon dates and assess their material associations before building Bayesian models. We present bespoke calibration curve mixtures for each major region, based on air mixtures from climate models. The models suggest that redwares burst onto the scene in the AD 600s in the Lake Titicaca Basin (Peru and Bolivia) and around the same time, snuff trays with the same iconography appeared in burials at San Pedro de Atacama (Chile). Other parts of the Andes first saw this material culture later, and only in the AD 900s was it clearly present in all regions. Around similar to AD 1040, Tiwanaku redwares were no longer used at Tiwanaku or in Moquegua. Residents of the Western Valleys immediately innovated new post-collapse styles derived from Tiwanaku redwares, appearing and fading away at different times in different valleys. A small community near Lake Titicaca maintained old traditions for generations, including the use of raised fields and Tiwanaku burials. We assess temporal alignments and disjunctures in order to highlight variability of Tiwanaku material culture, long assumed to be fairly homogeneous over space and time. This opens the door to more nuanced, generation-scale questions about the interaction networks that assembled and disassembled Tiwanaku.