Computed tomography (CT) provides rich 3D anatomical details but is often constrained by high radiation exposure, substantial costs, and limited availability. While standard chest X-rays are cost-effective and widely accessible, they only provide 2D projections with limited pathological information. Reconstructing 3D CT volumes from 2D X-rays offers a transformative solution to increase diagnostic accessibility, yet existing methods predominantly rely on synthetic X-ray projections, limiting clinical generalization. In this work, we propose AXON, a multi-stage diffusion-based framework that reconstructs high-fidelity 3D CT volumes directly from real X-rays. AXON employs a coarse-to-fine strategy, with a Brownian Bridge diffusion model-based initial stage for global structural synthesis, followed by a ControlNet-based refinement stage for local intensity optimization. It also supports bi-planar X-ray input to mitigate depth ambiguities inherent in 2D-to-3D reconstruction. A super-resolution network is integrated to upscale the generated volumes to achieve diagnostic-grade resolution. Evaluations on both public and external datasets demonstrate that AXON significantly outperforms state-of-the-art baselines, achieving a 11.9% improvement in PSNR and a 11.0% increase in SSIM with robust generalizability across disparate clinical distributions. Our code is available at https://github.com/ai-med/AXON.