The Multilevel Euler-Maruyama (ML-EM) method allows diffusion models to perform sampling at the computational cost of a single model evaluation.
March 26, 2026
Original Paper
Polynomial Speedup in Diffusion Models with the Multilevel Euler-Maruyama Method
arXiv · 2603.24594
The Takeaway
This provides a polynomial speedup for solving SDEs. Instead of dozens of expensive UNet passes, ML-EM uses a hierarchy of model sizes to achieve the same accuracy as the largest model with the cost of one pass, fundamentally changing the cost-benefit analysis of high-resolution diffusion generation.
From the abstract
We introduce the Multilevel Euler-Maruyama (ML-EM) method compute solutions of SDEs and ODEs using a range of approximators $f^1,\dots,f^k$ to the drift $f$ with increasing accuracy and computational cost, only requiring a few evaluations of the most accurate $f^k$ and many evaluations of the less costly $f^1,\dots,f^{k-1}$. If the drift lies in the so-called Harder than Monte Carlo (HTMC) regime, i.e. it requires $\epsilon^{-\gamma}$ compute to be $\epsilon$-approximated for some $\gamma>2$, th