Deterministic models for 3D hand pose reconstruction, whether single-staged or cascaded, struggle with pose ambiguities caused by self-occlusions and complex hand articulations. Existing cascaded approaches refine predictions in a coarse-to-fine manner but remain deterministic and cannot capture pose uncertainties. Recent probabilistic methods model pose distributions yet are restricted to single-stage estimation, which often fails to produce accurate 3D reconstructions without refinement. To address these limitations, we propose a coarse-to-fine cascaded diffusion framework that combines probabilistic modeling with cascaded refinement. The first stage is a joint diffusion model that samples diverse 3D joint hypotheses, and the second stage is a Mesh Latent Diffusion Model (Mesh LDM) that reconstructs a 3D hand mesh conditioned on a joint sample. By training Mesh LDM with diverse joint hypotheses in a learned latent space, our framework learns distribution-aware joint-mesh relationships and robust hand priors. Furthermore, the cascaded design mitigates the difficulty of directly mapping 2D images to dense 3D poses, enhancing accuracy through sequential refinement. Experiments on FreiHAND and HO3Dv2 demonstrate that our method achieves state-of-the-art performance while effectively modeling pose distributions.