Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity

Rigorous theoretical analysis reveals that our algorithm achieves $\widetilde{\mathcal{O}}(\mathrm{poly} \log d)$ overall time complexity, marking \emph{the first implementation with provable sub-linear complexity w.r.t. the data dimension $d$}. Our analysis is based on a generalized version of Girsanov's theorem and is compatible with both the SDE and probability flow ODE implementations. Our results shed light on the potential of fast and efficient sampling of high-dimensional data on fast-evolving modern large-memory GPU clusters.