We present algorithms for diffusion model sampling which obtain $δ$-error in $\mathrm{polylog}(1/δ)$ steps, given access to $\widetilde O(δ)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d_\star \mathrm{polylog}(1/δ))$ where $d_\star$ is the intrinsic dimension of the data. Further, under a non-uniform $L$-Lipschitz condition, the complexity reduces to $\widetilde O(L \mathrm{polylog}(1/δ))$. Our approach also yields the first $\mathrm{polylog}(1/δ)$ complexity sampler for general log-concave distributions using only gradient evaluations.

翻译：本文提出面向扩散模型采样的算法，在获得$\widetilde O(δ)$精度$L^2$分数估计的条件下，仅需$\mathrm{polylog}(1/δ)$步即可实现误差$δ$。该结果较此前所有方法实现了指数级提升。具体而言，在最小数据假设下，算法复杂度为$\widetilde O(d_\star \mathrm{polylog}(1/δ))$，其中$d_\star$为数据本征维度。进一步，在非均匀$L$-Lipschitz条件下，复杂度可降至$\widetilde O(L \mathrm{polylog}(1/δ))$。本方法还首次实现了仅通过梯度评估即可对一般对数凹分布进行$\mathrm{polylog}(1/δ)$复杂度采样。