Abstract
Methods & Inverse Problems
The following table summarizes the 14 benchmarked methods in InverseBench. They require different levels of properties of the forward model of the inverse problem.
| Category | Method | SVD | Pseudo inverse | Linear | Gradient |
|---|---|---|---|---|---|
| Linear guidance | DDRM | ✓ | ✓ | ✓ | -- |
| DDNM | ✗ | ✓ | ✓ | -- | |
| ΠGDM | ✗ | ✓ | ✗ | -- | |
| General guidance | DPS | ✗ | ✗ | ✗ | ✓ |
| LGD | ✗ | ✗ | ✗ | ✓ | |
| DPG | ✗ | ✗ | ✗ | ✗ | |
| SCG | ✗ | ✗ | ✗ | ✗ | |
| EnKG | ✗ | ✗ | ✗ | ✗ | |
| Variable-splitting | DiffPIR | ✗ | ✗ | ✗ | ✓ |
| PnP-DM | ✗ | ✗ | ✗ | ✓ | |
| DAPS | ✗ | ✗ | ✗ | ✓ | |
| Variational Bayes | RED-diff | ✗ | ✗ | ✗ | ✓ |
| Sequential Monte Carlo | FPS | ✗ | ✗ | ✓ | -- |
| MCGDiff | ✓ | ✓ | ✓ | -- |
Characteristics of different inverse problems in InverseBench, from left to right: whether the forward model is linear, whether one can compute the SVD from the forward model, whether the inverse problem operates in the complex domain, whether the forward model can be solved in closed form, whether one can access gradients from the forward model, and the noise type.
| Problem | Linear | SVD | Complex domain | Closed-form forward | Gradient access | Noise type |
|---|---|---|---|---|---|---|
| Linear inverse scattering | ✓ | ✓ | ✓ | ✓ | ✓ | Gaussian |
| Compressed sensing MRI | ✓ | ✗ | ✓ | ✓ | ✓ | Real-world |
| Black hole imaging | ✗ | ✗ | ✗ | ✓ | ✓ | Non-additive |
| Full waveform inversion | ✗ | ✗ | ✗ | ✗ | ✓ | Noise-free |
| Navier-Stokes equation | ✗ | ✗ | ✗ | ✗ | ✗ | Gaussian |
Qualitative Visualization
Visual examples for each problem. In the linear inverse scattering task, PnP diffusion prior methods can generate shaper images than the traditional baseline FISTA. For black hole imaging, the baselines are blurrier than plug-in-plug diffusion prior methods. Full waveform inversion: Adam\(^*\) and LBFGS\(^*\) are initialized from Gaussian blurred ground truth. With random or constant initialization, these optimization methods simply fail. Navier-Stokes equation: PnP diffusion prior methods capture more rich flow feature than the conventional baseline.
Experimental Results
Failures of PnPDM methods
Illustration of the failures of PnPDP methods (DAPS as an example) on full waveform inversion. With a small learning rate, DAPS is numerically stable but does not solve the inverse problem effectively. With a slightly larger learning rate, DAPS produces a noisy velocity map that breaks the stability condition of the PDE solver, resulting in a complete failure.
Comparison to traditional baseline
Relative performance of plug-and-play diffusion prior methods compared with traditional baselines under different levels of measurement sparsity on different tasks. Metrics are averaged over multiple PnPDP methods. The performance difference increases in general as the measurement becomes sparser.
PnPDM method on out-of-distribution test samples
PnPDP methods on out-of-distribution test samples. (a) Black-hole imaging problem on digits inputs; and (b) inverse scattering on sources that contain 9 cells, while the prior model is trained on images with 1 to 6 cells.
Acknowledgments
This research is funded in part by NSF CPS Grant 1918655, NSF Award 2048237, NSF Award 2034306 and Amazon AI4Science Discovery Award. H.Z. is supported by the PIMCO and Amazon AI4science fellowship. Z.W. is supported by the Amazon AI4Science fellowship. B.Z. and W.C. are supported by the Kortschak Scholars Fellowship. B.F. is supported by the Pritzker Award and NSF Graduate Research Fellowship. Z.E.R. And C.Z. are supported by a Packard Fellowship from the David and Lucile Packard Foundation. We thank Ben Prather, Abhishek Joshi, Vedant Dhruv, C.K. Chan, and Charles Gammie for the synthetic blackhole images GRMHD dataset used here, generated under NSF grant AST 20-34306.
BibTeX
@inproceedings{
zheng2025inversebench,
title={InverseBench: Benchmarking Plug-and-Play Diffusion Models for Scientific Inverse Problems},
author={Hongkai Zheng and Wenda Chu and Bingliang Zhang and Zihui Wu and Austin Wang and Berthy Feng and Caifeng Zou and Yu Sun and Nikola Borislavov Kovachki and Zachary E Ross and Katherine Bouman and Yisong Yue},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=U3PBITXNG6}
}