Formal guarantees for BAM’s learned conditional flow map

Establish formal guarantees for the learned conditional flow map implemented by the Bayesian Anything Model (BAM), including guarantees relevant to the quality of its posterior samples.

Background

The Bayesian Anything Model (BAM) is a 36-million-parameter, operator-conditioned generative model designed to draw posterior samples for computational imaging problems in only a few network evaluations. It is trained as a conditional flow map that transports a Gaussian reference distribution to an image posterior conditioned on the measurement, forward operator, and noise level.

Although the paper evaluates BAM empirically across several linear inverse problems and reports strong sample-quality and computational results, it does not establish theoretical convergence, accuracy, or posterior-correctness guarantees for the learned conditional flow map. The authors explicitly identify formal guarantees as unresolved, making this a direct open problem concerning the reliability of BAM beyond the reported experiments.

References

Finally, posterior sample quality was assessed empirically, and formal guarantees for the learned conditional flow map remain open.

— BAM! Bayesian Anything Model: a foundation model for generative computational imaging  (2609.39660 - Spagnoletti et al., 30 Sep 2026) in Section Conclusion and limitations

Establishing corresponding approximation and learning guarantees for dependent observations is left for future work.

— Neural Estimation of Summary Statistics for Simulation-Based Inference with Non-Asymptotic Guarantees  (2610.13031 - Li et al., 9 Oct 2026) in Section Discussion