The score-based generative model (SGM) has received significant attention in the field of medical imaging, particularly in the context of limited-angle computed tomography (LACT). Traditional SGM approaches achieved robust reconstruction performance by incorporating a substantial number of sampling steps during the inference phase. However, these established SGM-based methods require large computational cost to reconstruct one case. The main challenge lies in achieving high-quality images with rapid sampling while preserving sharp edges and small features. In this study, we propose an innovative rapid-sampling strategy for SGM, which we have aptly named the time-reversion fast-sampling (TIFA) score-based model for LACT reconstruction. The entire sampling procedure adheres steadfastly to the principles of robust optimization theory and is firmly grounded in a comprehensive mathematical model. TIFA’s rapid-sampling mechanism comprises several essential components, including jump sampling, time-reversion with re-sampling, and compressed sampling. In the initial jump sampling stage, multiple sampling steps are bypassed to expedite the attainment of preliminary results. Subsequently, during the time-reversion process, the initial results undergo controlled corruption by introducing small-scale noise. The re-sampling process then diligently refines the initially corrupted results. Finally, compressed sampling fine-tunes the refinement outcomes by imposing regularization term. Quantitative and qualitative assessments conducted on numerical simulations, real physical phantom, and clinical cardiac datasets, unequivocally demonstrate that TIFA method (using 200 steps) outperforms other state-of-the-art methods (using 2000 steps) from available [0°, 90°] and [0°, 60°]. Furthermore, experimental results underscore that our TIFA method continues to reconstruct high-quality images even with 10 steps. Our code at https://github.com/tianzhijiaoziA/TIFADiffusion.