Recently studies have witnessed great progresses of generative modeling in medical imaging reconstruction like fast MRI and low-dose CT, etc. Particularly, the series of works from denoising autoencoders to denoising score matching as well as score-based diffusion model exhibits great promising performance in reconstruction quality and algorithm robustness. In this talk, we will first review the relationship among these algorithms. Then, we reveal the underlying ideas that substantially contribute to the performance improvements, such as constructing high-dimensional space and conducting on data samples with different geometrical properties.