  The local distance ladder estimate of the Hubble constant ($H_0$) is
important in cosmology, given the recent tension with the early universe
inference. We estimate $H_0$ from the Type Ia supernova (SN~Ia) distance
ladder, inferring SN~Ia distances with the hierarchical Bayesian SED model,
BayeSN. This method has a notable advantage of being able to continuously model
the optical and near-infrared (NIR) SN~Ia light curves simultaneously. We use
two independent distance indicators, Cepheids or the tip of the red giant
branch (TRGB), to calibrate a Hubble-flow sample of 67 SNe~Ia with optical and
NIR data. We estimate $H_0 = 74.82 \pm 0.97$ (stat) $\pm\, 0.84$ (sys)
km\,s$^{-1}$\,Mpc$^{-1}$ when using the calibration with Cepheid distances to
37 host galaxies of 41 SNe~Ia, and $70.92 \pm 1.14$ (stat) $\pm\,1.49$ (sys)
km\,s$^{-1}$\,Mpc$^{-1}$ when using the calibration with TRGB distances to 15
host galaxies of 18 SNe~Ia. For both methods, we find a low intrinsic scatter
$\sigma_{\rm int} \lesssim 0.1$ mag. We test various selection criteria and do
not find significant shifts in the estimate of $H_0$. Simultaneous modelling of
the optical and NIR yields up to $\sim$15\% reduction in $H_0$ uncertainty
compared to the equivalent optical-only cases. With improvements expected in
other rungs of the distance ladder, leveraging joint optical-NIR SN~Ia data can
be critical to reducing the $H_0$ error budget.
