$S_8$ from Tully-Fisher, fundamental plane, and supernova distances agree with Planck

Peculiar velocity measurements constrain the parameter combination $f{\sigma }_8$, the product of the linear growth rate $f$ and the fluctuation amplitude ${\sigma }_8$. Under the approximation that $f$ is a monotonic function of ${\mathrm{\Omega }}_{\mathrm{m}}$, this can be related to $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_{\mathrm{m}}\mathrm{/}0.3}$, enabling direct comparison with weak lensing and cosmic microwave background results. We exploit this by using three classes of direct-distance tracers – the Tully-Fisher relation, the fundamental plane, and Type~Ia supernovae – to infer peculiar velocities. A unified hierarchical forward model jointly calibrates each distance indicator and a linear theory reconstruction of the local Universe. This is the first consistent Bayesian analysis to combine all three major classes of distance indicators within a common framework, enabling cross-checks of systematics across diverse galaxy populations. All three tracers yield consistent values of $S_8$ that are also in agreement with Planck. Our joint constraint is $S_8=0.819\pm 0.030$, with the uncertainty dominated by the 2M++ galaxy field. These results demonstrate that peculiar velocity surveys provide a robust, consistent measurement of $S_8$, and support concordance with the cosmic microwave background.