Score matching (Hyvärinen 2005) provides a way to fit an energy-based model p_θ(x) ∝ exp(−E_θ(x)) without computing the intractable partition function Z = ∫exp(−E_θ(x))dx. The score function s(x) = ∇_x log p(x) = −∇_x E(x) is independent of Z. The score matching objective J(θ) = E_p[½‖s_θ(x)‖² + tr(∇_x s_θ(x))] matches the model score to the data score. Denoising score matching (Vincent 2011) avoids computing the trace term: instead train s_θ(x̃,σ) ≈ (x−x̃)/σ² where x̃ = x + ε, ε~N(0,σ²I). Langevin dynamics then samples from the learned distribution: x_{t+1} = x_t + ε∇_x log p(x_t) + √(2ε)z. The arrows show the estimated score field; particles follow Langevin MCMC.