Ever since Stebbins declared polyploid plants evolutionary "dead ends," the link between polyploidization and diversification has been controversial. While several whole genome multiplication (WGM) events seem to pre-date rapid species accumulation in many clades, the existence of long lags between WGMs and diversification make the drawing of direct links difficult. Previous work has relied on nodal or temporal distances between WGMs and diversification on phylogenies, with the difficulty that there is no a priori cut-off of how long a diversification lag should be. A more robust test of the lag hypothesis, one which does not require hypotheses of lag length, can be constructed within the framework of hidden state-dependent speciation and extinction (HiSSE) models. Specifically, the SSE framework of HiSSE allows tests of whether hypothetical "hidden," or unobserved, characters may better explain the data than observed characters under study. In the context of the lag hypothesis, we construct a lag model where observed ploidy states are labeled 0 and 1 (diploid and polyploid) and hidden states are labeled A and B (low diversification rate class and high diversification rate class). Species start in combined state 0A, and can polyploidize to transition to state 1A, but they must undergo an additional transition from state 1A to state 1B in order to diversify, with the time taken to undertake this transition simulating a lag. The lag model is also directly comparable with all other types of SSE models, such as one with diversification but no lag (transitions to polyploidy immediately cause diversification shifts, with no hidden states) and one where polyploidy is unlinked with diversification (shifts between states 0A, 0B, 1A, and 1B are all possible and equally likely). Here, we apply the lag model to test the relationship between polyploidization and diversification in the well-characterized clades of Brassicaceae and Caryophyllales. Preliminary tests suggest strong support for ploidy-independent models in which ploidy states and all diversification rate classes are allowed to freely transition along the tree regardless of ploidy state. This suggests that polyploidy is not associated with diversification shifts, and that other traits associated with polyploidy, such as shifts in breeding system, identified in recent work may better explain the data.