The diffusion model and its applications in bioinformatics

In recent years, diffusion models have garnered significant attention, achieving remarkable success in many fields such as computer vision, natural language processing, and bioinformatics, while also demonstrating broad application prospects. In this survey paper, we elucidate the probabilistic significance of diffusion models, outline their development processes, and provide a detailed account of their applications in bioinformatics. In the beginning, we define the forward and backward processes of diffusion models from the perspective of stochastic differential equations, and we elaborate on the probabilistic principles of three types of diffusion models: NCSN, DDPM, and DDIM, in conjunction with the derivation of score matching. Due to their powerful generative capabilities, diffusion models have found extensive applications in bioinformatics, particularly in the areas of transcriptomics and protein research. Furthermore, these models not only excel in imputing and denoising single-cell and spatial transcriptomic sequencing data but also demonstrate significant effectiveness in protein design, structure prediction, and the design of small molecules and peptide drugs.