Finite-Budget Representative Sampling from Diffusion Models

Diffusion models are usually sampled with independent denoising trajectories, but under tight inference budgets an iid batch can duplicate common outcomes and miss important probability regions. We formulate finite-budget sampling as the construction of a representative empirical measure, separating two goals: placing support across density-separated regions and assigning weights for accurate expectation estimation. Without access to the original data, we learn a kernel from model samples that treats samples connected through high-density regions as similar and use it during sampling to guide the batch toward distribution matching and nonredundant coverage. We then assign quadrature weights to the sampled points for expectation estimation. Experiments show that, under limited sampling budgets, our method improves support coverage and produces weights that better represent the model distribution. When used in Monte Carlo tree search, the resulting weighted batches yield more accurate action-value estimates.