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The lateral cephalogram (LC)-based volumetric image estimation is feasible to relieve the hazardous radiation exposure and study patient-specific 3D morphology of craniofacial structures in clinical orthodontics. The deep learning-based approach has potential in volumetric reconstruction of computed tomography in recent years. However, existing work employed the cross-dimensional feature transformation by channel concatenation or element rearrangement, without considering the voxel-wise semantic inference regarding a variety of anatomical tissues. The deep learning-based model relied on synthetic paired 2D X-rays and 3D volumes and required an additional domain adaption module to generalize to clinical data. This work customizes a cross-dimensional discrete embedding mapping model (CD<inline-formula><tex-math notation="LaTeX">^{2}</tex-math></inline-formula>EM) for 3D craniofacial volumetric image estimation from a 2D LC. The vector quantization-based discrete embedding and the learnable codebook are introduced to relieve redundancy in feature representation for voxel-wise inference of craniofacial structures, with codes indicating the probability distribution of a variety of anatomical tissues. We devise an unsupervised learning scheme to generalize the model to clinically obtained LCs. We demonstrate the advantage and effectiveness of the discrete coding and mapping scheme on the clinical LC-based voxel-wise craniofacial volumetric image estimation.