We present an algorithmic framework for high-accuracy sampling using unbiased stochastic queries, with two main applications:

(1) Algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. (ICML 2026 outstanding paper, https://arxiv.org/abs/2602.01338)

(2) High-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{polylog}(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic gradients with subexponential tails. Notably, this exhibits a separation with the problem of convex optimization, where stochasticity (even additive Gaussian noise) in the gradient oracle incurs $\mathrm{poly}(1/\delta)$ queries. (CoLT 2026, https://arxiv.org/abs/2602.14342)