Hilbert-Scale Stability of Posterior Diffusion Priors for Ill-Posed Signal Recovery
Indirect and noisy observations are difficult to invert when the forward operator smooths out the unknown signal. In this case, the unstable modes are precisely the modes that the data reveals least, thus the success of any reconstruction method depends on how prior information interacts with the geometry of the operator across regularity scales. Diffusion priors have become ubiquitous for such problems; however, the current theory still does not determine when a learned score remains informative under ill-posed forward operators. In this paper, we study posterior diffusion for linear inverse problems on Hilbert scales and derive a stability theory under an explicit score-amplification co...
| Authors | Bahman Moraffah, Raha Moraffah |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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