The Score-Based View — Gradients, SDEs, and Why Denoising Learns Direction
DDPM looks like a clever trick: predict noise, subtract it, repeat. The score-based view reveals it as something deeper — the denoiser is secretly learning the gradient of the data distribution, the arrow that points from anywhere in image space toward "more like a real image." Two research threads, denoising and score matching, turned out to be the same thing seen from different angles, and their unification under stochastic differential equations is what every modern sampler and flow-matching method builds on.
The denoiser is secretly learning the score — the gradient of log-probability pointing toward more-plausible images. Langevin dynamics, why denoising and score matching are the same computation, and the continuous limit: a reverse-time SDE and its deterministic twin, the probability flow ODE, where fast sampling and flow matching live.