Detecting compression fractures in thick-slice CT images (e.g., 5.0 mm slices) is challenging due to the coarse resolution along the slice direction. This study proposes a 3D conditional diffusion model-based slice interpolation method to improve vertebral height estimation and compression fracture detection from thick-slice CT images. We conducted comparative evaluations against conventional GAN-based approaches. To assess clinical utility, we compared vertebral height measurement accuracy and fracture detection performance across interpolated images generated by each method. Our conditional diffusion model (cDiff) achieved the lowest mean absolute error in vertebral height measurements (0.79 ± 0.77 mm), significantly outperforming GAN-based methods ( \(p<0.005\) ). The GAN-based models often reconstructed fractured vertebrae with exaggerated height resembling normal anatomy, resulting in lower detection sensitivity. In contrast, the diffusion model successfully captured diverse fracture morphologies—such as wedge, fish, and flat vertebrae—achieving the highest F1 score of 88.2% with a sensitivity of 93.0% (93/100) and a specificity of 97.3% (649/667). The proposed method enables early detection of latent compression fractures that are potentially overlooked in typical screening workflows where only thick-slice CT images are available.