Monocular 3D human pose and shape estimation is an ill-posed problem since multiple 3D solutions can explain a 2D image of a subject. Recent approaches predict a probability distribution over plausible 3D pose and shape parameters conditioned on the image. We show that these approaches exhibit a trade-off between three key properties: (i) accuracy - the likelihood of the ground-truth 3D solution under the predicted distribution, (ii) sample-input consistency - the extent to which 3D samples from the predicted distribution match the visible 2D image evidence, and (iii) sample diversity - the range of plausible 3D solutions modelled by the predicted distribution. Our method, HuManiFlow, predicts simultaneously accurate, consistent and diverse distributions. We use the human kinematic tree to factorise full body pose into ancestor-conditioned per-body-part pose distributions in an autoregressive manner. Per-body-part distributions are implemented using normalising flows that respect the manifold structure of SO(3), the Lie group of per-body-part poses. We show that ill-posed, but ubiquitous, 3D point estimate losses reduce sample diversity, and employ only probabilistic training losses. HuManiFlow outperforms state-of-the-art probabilistic approaches on the 3DPW and SSP-3D datasets.