ICML 2025

S4S: Solving for a Fast Diffusion Model Solver
Eric Frankel 1 Sitan Chen 2 Jerry Li 1 Pang Wei Koh 1 3 Lillian J. Ratliff 1 Sewoong Oh 1
Abstract
Diffusion models (DMs) create samples from a
data distribution by starting from random noise
and iteratively solving a reverse-time ordinary dif-
ferential equation (ODE). Because each step in
the iterative solution requires an expensive neural
function evaluation (NFE), there has been sig-
nificant interest in approximately solving these
diffusion ODEs with only a few NFEs without
modifying the underlying model. However, in the
few NFE regime, we observe that tracking the
true ODE evolution is fundamentally impossible
using traditional ODE solvers. In this work, we
propose a new method that learns a good solver
for the DM, which we call Solving for the Solver
(S4S). S4S directly optimizes a solver to obtain
good generation quality by learning to match the
output of a strong teacher solver. We evaluate S4S
on six different pre-trained DMs, including pixel-
space and latent-space DMs for both conditional
and unconditional sampling. In all settings, S4S
uniformly improves the sample quality relative to
traditional ODE solvers. Moreover, our method
is lightweight, data-free, and can be plugged in
black-box on top of any discretization schedule
or architecture to improve performance. Building
on top of this, we also propose S4S-Alt, which
optimizes both the solver and the discretization
schedule. By exploiting the full design space of
DM solvers, with 5 NFEs, we achieve an FID
of 3.73 on CIFAR10 and 13.26 on MS-COCO,
representing a 1.5× improvement over previous
training-free ODE methods.
1University of Washington
2Harvard University
3Allen
Institute for AI. Correspondence to:
Eric Frankel <er-
icsf@cs.washington.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(s).
Figure 1. Abstraction of the S4S approach. In low-NFE environ-
ments, co...