Score-Based Generative Modeling via Stochastic Differential Equations: How Continuous SDEs and Score Matching Unify Diffusion Models
Diffusion and score-based models represent one of the foundational paradigms of modern generative artificial intelligence, underpinning systems across image synthesis, video generation, audio modeling, and continuous multimodal representations. For years, generative diffusion was approached from two distinct perspectives: discrete-step denoising diffusion probabilistic models (DDPM) pioneered by Sohl-Dickstein et al. and Ho et al., and score matching with Langevin dynamics (SMLD / NCSN) introduc

