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InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences
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Introduces InverseBench, a benchmark evaluating 14 plug-and-play diffusion prior algorithms against domain-specific baselines on five scientific inverse problems (linear inverse scattering, CS-MRI, black hole imaging, FWI, Navier-Stokes).
Problem
Plug-and-play diffusion priors are mostly evaluated on natural image restoration; their performance on scientific inverse problems with nonlinear, PDE-based, or non-Gaussian forward models is unexplored.
Approach
A modular benchmark that curates five physics-based scientific inverse problems with diverse forward models (linear, closed-form nonlinear, PDE solvers, black-box), pretrains a diffusion prior per problem, and evaluates 14 PnP diffusion methods with accuracy, efficiency, and ranking metrics against classical and end-to-end baselines.
Key results
- On linear inverse scattering with 60 receivers, DDNM reaches 29.24 dB PSNR, outperforming FISTA-TV at 20.94 dB.
- On FWI, DiffPIR achieves the best PSNR among PnP methods (16.11 dB) but classical LBFGS initialized from blurred ground truth reaches 23.40 dB, outperforming PnP methods.
- On Navier-Stokes, EnKG attains the lowest relative L2 error (0.120 at x2 subsampling, noise-free), while DAPS and PnP-DM degrade due to PDE solver instability.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PnP diffusion prior methods instead of conventional baselines | InverseBench scientific inverse problems · Scientific inverse problems overall | Recovery accuracy | Helped |
| Initialize classic optimization baselines with a heavily blurred ground-truth image rather than randomly or constantly | Full waveform inversion · Full waveform inversion | Relative L2: 0.333 (0.086) -> 0.089 (0.021); 0.070 (0.023) | Hurt |
| Use PnP-DM instead of E2E-VarNet | CS-MRI · CS-MRI, ×4 simulated noiseless | PSNR: 31.80 (3.473) vs 33.40 (2.097) | Hurt |
| Use PnP-DM instead of EHT-Imaging | Black hole imaging · Black hole imaging | PSNR: 21.72 (3.39) -> 24.25 (3.45) | Helped |
| Use PnP-DM instead of EHT-Imaging | Black hole imaging · Black hole imaging, 100% observation time | PSNR: 24.28 (3.63) -> 26.07 (3.70) | Helped |
| Use DAPS or PnP-DM, which make more forward-model gradient queries, instead of simpler PnP methods | PnP diffusion prior methods · Problems with closed-form forward models | Accuracy | Helped |
| Use DAPS or PnP-DM with PDE-based forward models | PnP diffusion prior methods · Full waveform inversion and Navier-Stokes | Accuracy | Hurt |
| Increase measurement sparsity | Top PnP diffusion prior methods relative to baselines · Inverse problems with varying measurement sparsity | Performance gain over baselines | Helped |
| Change the CS-MRI subsampling pattern from vertical to horizontal lines | PnP diffusion prior methods · CS-MRI | PSNR variation: 0.48dB | No clear effect |
| Change the CS-MRI subsampling pattern from vertical to horizontal lines | End-to-end methods · CS-MRI | PSNR variation: 9.58dB | Hurt |
| Use a source outside the diffusion prior distribution | PnP diffusion prior methods · Out-of-distribution sources | Recovery fidelity | Hurt |
| Use PnP methods with multiple forward-model queries instead of DPS | PnP diffusion prior methods · Inverse problems overall | Accuracy | Helped |
Surprising findings
- DAPS and PnP-DM perform poorly on PDE-constrained problems (FWI, Navier-Stokes) despite being top performers on closed-form forward models, due to numerical instability from stability conditions of the PDE solver.
- PnPDP methods are reported to be more robust than end-to-end methods when the CS-MRI sampling pattern changes (average PSNR change 0.48 dB vs 9.58 dB for end-to-end).
Limitations
- PnPDP methods do not account for PDE solver stability (CFL) conditions, causing instability in FWI and Navier-Stokes.
- PnPDP methods struggle to recover out-of-distribution sources, producing outputs biased toward the prior (e.g., black hole ring).
- Most PnPDP methods are computationally slower than conventional baselines.
Experimental setup
Datasets: GRMHD simulated black hole images CurveFaultB fluorescence microscopy simulator images (HL60) fastMRI knee fastMRI+ Navier-Stokes Gaussian random field initial vorticity
Benchmarks: InverseBench (linear inverse scattering, CS-MRI, black hole imaging, FWI, Navier-Stokes)
Metrics: PSNR SSIM relative L2 error data misfit chi-squared closure statistics blur PSNR mAP50 ranking score runtime and forward-evaluation counts
Baselines: FISTA-TV DDRM DDNM ΠGDM DPS LGD DiffPIR RED-diff
Builds on: DPS DDRM DDNM DAPS PnP-DM
Closest papers by meaning
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.89)
- DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models (NeurIPS 2024 · similarity 0.89)
- Inference-Time Search Using Side Information for Diffusion-Based Image Reconstruction (NeurIPS 2026 · similarity 0.88)
- Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Linear Extrapolation (NeurIPS 2025 · similarity 0.88)
- Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration (NeurIPS 2026 · similarity 0.88)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.88)
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