Scope of InverseBench findings

Zheng et al.'s InverseBench reports 14 plug-and-play diffusion-prior algorithms and domain-specific baselines on five selected cases: first-Born optical scattering, raw multi-coil knee MRI, black-hole very-long-baseline interferometry, full waveform inversion, and two-dimensional vorticity-form Navier–Stokes inversion. For these experiments, the authors report that diffusion-prior methods often outperform conventional baselines when the training data are suitable, while a classical full-waveform-inversion optimizer initialized from a smoothed ground truth outperforms the tested diffusion-prior methods. In cases with closed-form forward models, methods using more forward-gradient queries can be more accurate and more expensive; the paper reports that this trend fails for its numerical PDE cases. Its Navier–Stokes split has one validation case and ten test cases. The paper reports step-size/Courant–Friedrichs–Lewy (CFL) failures in its PDE experiments. Its Figure 5 out-of-distribution diagnostics feed digit images to a black-hole prior trained on simulated black-hole images, and nine-cell scattering sources to a prior trained on one-to-six-cell sources; for the black-hole case, the authors report outputs with the prior's characteristic ring feature. These are empirical observations for the named data, solvers, methods, tuning protocol, and hardware; they establish no universal ranking, stability bound, posterior exactness, risk-transfer bound, or robustness theorem.

There is a first-Born notation discrepancy between the paper and its released implementation. Appendix B.1 defines a contrast-dependent total field and then displays a sensor equation with that field multiplied by the contrast, which does not itself exhibit a fixed linear map. The pinned implementation instead passes the fixed incident field into the sensor-propagation routine and constructs its cached linear matrix from that fixed field. This page therefore identifies the implemented benchmark as the first-Born linear case and does not infer linearity from the printed contrast-dependent expression.

Benchmark specification and reporting protocol

Risk under a named joint evaluation law

Learned estimators, score fields, and posterior samplers carry no automatic guarantee

Operator and prior mismatch are distinct and imply no automatic robustness bound

Solver admissibility and CFL thresholds are model-specific

Exact diffusion scores versus learned or plug-in approximations

Zheng et al., InverseBench, ICLR 2025, full paper and appendices

InverseBench implementation, pinned inverse_scatter.py source