High-accuracy sampling for diffusion models and log-concave distributions
This provides a breakthrough for efficient sampling in machine learning, enabling faster and more scalable generation and inference tasks.
The paper tackles the problem of sampling from diffusion models and log-concave distributions with high accuracy, achieving an exponential improvement in complexity to polylog(1/δ) steps under various data assumptions, such as reducing complexity to O(d_star polylog(1/δ)) for intrinsic dimension d_star.
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 $\widetilde O(d\,\mathrm{polylog}(1/δ))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\,\mathrm{polylog}(1/δ))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\,\mathrm{polylog}(1/δ))$. Our approach also yields the first $\mathrm{polylog}(1/δ)$ complexity sampler for general log-concave distributions using only gradient evaluations.