Unlock: Score Matching

Hyvärinen 2005: train a model to estimate the score (gradient of log density) without computing the normalization constant. Integration by parts converts the intractable density-matching loss into a tractable gradient-based objective. Sliced score matching makes the Jacobian-trace term scale, denoising score matching reparameterizes the loss as ε-regression, and Tweedie's formula identifies the score with a posterior-mean denoiser. Together these are the training half of every modern diffusion model and energy-based model.