Boosting a near-correct sampler to improve epsilon dependence

Develop a generic boosting procedure for generative modeling that, given a sampling oracle whose output distribution is already sufficiently close (e.g., in total variation distance) to a target distribution, refines the oracle to achieve arbitrarily small accuracy epsilon in total variation, analogous to boosting in supervised learning. Such a procedure should enable improving the current exponential dependence on 1/epsilon in the diffusion-model-based learning of Gaussian mixtures to a logarithmic dependence on 1/epsilon, matching prior rates.

Background

The paper’s algorithm learns well-conditioned Gaussian mixtures via diffusion models and score matching but currently incurs exponential dependence on 1/epsilon, unlike prior methods that achieve logarithmic dependence. The authors highlight that a generic post-processing or refinement mechanism for samplers—which strengthens an already-approximately-correct sampler to arbitrarily high accuracy—could close this gap.

They explicitly pose the question of whether a boosting-like procedure exists for samplers that are already close to the target distribution, and note that a positive answer would yield a generic way to improve the epsilon dependence of their algorithm to match the best known rates.