Early analyses of exoplanet statistics from the Kepler Mission revealed that a single population of multiple-planet systems with low mutual inclinations (1-2 deg) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. Ten years later, the explanation of this so-called “Kepler dichotomy” remains uncertain. The leading hypothesis is that there are at least two (but perhaps a continuum) of sub-populations of intrinsically multi-planet systems with different mutual inclination dispersions. However, the statistical properties and physical origins of these sub-populations are still poorly constrained. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting Transit Duration Variations (TDVs) of the Kepler planet population. Planet-planet interactions drive orbital precession that leads to slow drifts of a planet’s transit duration. These TDV signals are inclination-sensitive and detectable for nearly two dozen Kepler planets. Using the Kepler TDV detections as our observational constraint, we consider simulated planet populations from two empirically-calibrated forward modeling frameworks with different assumptions for the mutual inclination distributions. We compute the TDV statistics (specifically, the frequency of detectable TDV signals) of the simulated planet populations and compare them to TDVs of the observed Kepler planets. We find strong evidence for a non-dichotomous, multiplicity-dependent distribution of relatively low (< 10 deg) mutual inclinations. These results place strong constraints on the dynamical mechanisms responsible for the excitation of Kepler planet mutual inclinations; we review the relevant theories and highlight those that are most compatible with the data.