Abstract Dramatic spatial, temporal and taxonomic variation in biodiversity is ultimately explained by differences in speciation and extinction rates. Mammals represent a ∼200 My old radiation that resulted in over 6500 extant species, with stark temporal, spatial and taxonomic heterogeneity in biodiversity. Throughout their history, every mammal lineage is expected to have undergone diversification rates that vary instantaneously in time resulting from the complex interplay of context-specific extrinsic factors ( e.g ., K-Pg mass extinction event, rise of angiosperms) with their evolving ecologies ( e.g ., body size, diet). When studying the diversification history of a clade, however, mathematical and computational limitations have hindered inference of such a flexible birth-death model where speciation and extinction rates evolve continuously along a phylogenetic tree. Here we overcome these challenges by implementing a series of phylogenetic models in which speciation and extinction rates are inherited and diffuse following a latent Geometric Brownian motion process. We enable full Bayesian inference using data augmentation techniques to sample from the posterior distribution of model parameters, including augmented phylogenetic trees and validate using simulations. Using a genome-informed time-calibrated tree for over 4000 Mammals species, we are able to estimate a complete and fine-grained picture of the variation in diversification rates that captures both global and lineage specific effects. We find that, contrary to the idea of a suppressed mammalian diversification before the K-Pg mass extinction event ( i.e ., explosive- or delayed-rise), mammal speciation rates dramatically increased around 10-20 My before the K-Pg. Our new model opens exciting possibilities in disentangling the drivers behind variation in diversification and assaying how small-scale processes scale-up to macroevolutionary dynamics.