Stanford CME296 Diffusion & Large Vision Models | Spring 2026 | Lecture 2 - Score matching

Score matching provides a robust paradigm for generative modeling by estimating the gradient of the log-probability density function, known as the score, to guide sampling toward high-density data regions. Because the true score is often intractable, denoising score matching trains models on noise-perturbed data to approximate the score function effectively. Annealed Langevin dynamics enhances this process by utilizing multiple noise levels, starting with high noise to establish global structure before refining details with lower noise. Furthermore, the continuous formulation of these models through stochastic differential equations and probability flow ordinary differential equations offers a unified framework. This approach allows for more efficient sampling by leveraging advanced numerical solvers, such as DPM Solver, which optimize the trade-off between computational budget and sample quality without requiring model retraining.