ICML 2025

Integrating Intermediate Layer Optimization and Projected Gradient Descent
for Solving Inverse Problems with Diffusion Models
Yang Zheng 1 Wen Li 1 Zhaoqiang Liu 1
Abstract
Inverse problems (IPs) involve reconstructing sig-
nals from noisy observations. Recently, diffu-
sion models (DMs) have emerged as a powerful
framework for solving IPs, achieving remarkable
reconstruction performance. However, existing
DM-based methods frequently encounter issues
such as heavy computational demands and subop-
timal convergence. In this work, building upon
the idea of the recent work DMPlug (Wang et al.,
2024), we propose two novel methods, DMILO
and DMILO-PGD, to address these challenges.
Our first method, DMILO, employs intermediate
layer optimization (ILO) to alleviate the mem-
ory burden inherent in DMPlug. Additionally,
by introducing sparse deviations, we expand the
range of DMs, enabling the exploration of under-
lying signals that may lie outside the range of
the diffusion model. We further propose DMILO-
PGD, which integrates ILO with projected gra-
dient descent (PGD), thereby reducing the risk
of suboptimal convergence. We provide an intu-
itive theoretical analysis of our approaches under
appropriate conditions and validate their superi-
ority through extensive experiments on diverse
image datasets, encompassing both linear and
nonlinear IPs. Our results demonstrate signifi-
cant performance gains over state-of-the-art meth-
ods, highlighting the effectiveness of DMILO and
DMILO-PGD in addressing common challenges
in DM-based IP solvers.
1. Introduction
Inverse problems (IPs) represent a broad class of challenges
focused on reconstructing degraded signals, particularly
images, from noisy observations. These problems are of
1University of Electronic Science and Technology of China.
Correspondence to: Zhaoqiang Liu <zqliu12@gmail.com>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(s...