Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models

Yang Zheng, Wen Li, Zhaoqiang Liu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:78190-78207, 2025.

Abstract

Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion 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 suboptimal convergence. In this work, building upon the idea of the recent work DMPlug, 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 memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approaches under appropriate conditions and validate their superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zheng25h, title = {Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models}, author = {Zheng, Yang and Li, Wen and Liu, Zhaoqiang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {78190--78207}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zheng25h/zheng25h.pdf}, url = {https://proceedings.mlr.press/v267/zheng25h.html}, abstract = {Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion 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 suboptimal convergence. In this work, building upon the idea of the recent work DMPlug, 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 memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approaches under appropriate conditions and validate their superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.} }
Endnote
%0 Conference Paper %T Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models %A Yang Zheng %A Wen Li %A Zhaoqiang Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zheng25h %I PMLR %P 78190--78207 %U https://proceedings.mlr.press/v267/zheng25h.html %V 267 %X Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion 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 suboptimal convergence. In this work, building upon the idea of the recent work DMPlug, 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 memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approaches under appropriate conditions and validate their superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.
APA
Zheng, Y., Li, W. & Liu, Z.. (2025). Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:78190-78207 Available from https://proceedings.mlr.press/v267/zheng25h.html.

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