We have developed an approach integrating statistical rock physics with pressure and thermal history modeling for quantitative seismic interpretation (QSI). Extending the training data for lithofacies classification and deriving distributions for scenarios not available in the original training require knowledge about geologic processes affecting the elastic properties in the subsurface. We model pressure and thermal history and corresponding smectite to illite diagenesis with a basin model across Thunder Horse minibasin in the Gulf of Mexico. By comparing the mapped lithofacies with and without basin-modeling extrapolations against the results of a reference workflow, we found the value of integrating basin modeling results and statistical rock physics with QSI workflows. The reference workflow uses all available data from two wells in the QSI. The first workflow performs the same lithofacies classification with data from only a single well and does not account for spatial trends away from the well. In the second workflow, we use data from only a single well, the same well as in the first workflow, and bring in extrapolation from the basin and petroleum system modeling at the location of the second well. Results for the first workflow indicate significant differences with the reference workflow in the training data, the quality of the inverted impedance volumes, and the classified reservoir lithofacies. In the second workflow, the guided extrapolation of the training data accounts for spatial trends away from the well and the quality of the impedance inversion significantly improves. The predicted lithofacies map in this scenario shows only minor differences from the reference workflow, and the posterior probabilities of lithofacies show less uncertainty compared with the first workflow. The superiority of the second workflow demonstrates the added value of the integration workflow to QSI in cases of spatially limited well control.