From Regressors to Samplers via the Training Trajectory

Regression models are inexpensive to train compared to generative models, but leveraging them for sampling remains challenging. We show that using the training trajectory as the annealing path is theoretically grounded—corresponding to spectral filtering in continuous settings and low-degree projection in discrete ones, which for certain Boolean functions reduces exponential mixing to $O(d \log d)$. Empirically, this strategy improves sampling across synthetic and real tasks while being zero-cost.