A hybrid sampling framework that alternates between a predictor and corrector at each reverse-time step. The predictor is a numerical SDE solver (Euler-Maruyama, reverse diffusion, ancestral sampling) that estimates the next sample along the reverse diffusion trajectory. The corrector is a score-based MCMC step (Langevin dynamics using the score model) that refines the sample’s marginal distribution at the current noise level.
This framework unifies and generalizes the sampling procedures of both SMLD and DDPM under a single algorithmic umbrella. By decoupling the coarse reverse-time evolution (predictor) from the local distributional refinement (corrector), the method achieves higher sample quality than either component alone.
Algorithm
- Predictor: Apply a numerical SDE solver to estimate x_{t-Δt} from x_t using the learned score function.
- Corrector: Run M steps of Langevin MCMC using the score model s_θ(x, t-Δt) with step size controlled by signal-to-noise ratio r.
- Return the refined sample after processing all reverse time steps.
Key Properties
- Consistently outperforms predictor-only or corrector-only sampling
- One corrector step per predictor is more beneficial than doubling the number of predictors
- Generalizes both SMLD and DDPM sampling procedures
- Signal-to-noise ratio r controls the corrector step size
- Introduced by Song et al. (2021)