Understanding and enhancing diffusion model: a quantification of its generalizability, and a provably scalable test-time scaling method

The first part characterizes how continuous diffusion models generate beyond their training examples using the empirical distribution itself, clarifying their inductive bias without a population-limit assumption. The second introduces reward-guided remasking for discrete generation without changing model weights. The proposed sampler corrects earlier choices and comes with robustness guarantees under noisy process verification, contrasting its quadratic complexity with potentially exponential error accumulation in common selection heuristics.