Backward-Consistent Diffusion Sampling for Sparsely Observed PDE Inverse Problems
Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for which generative machine learning methods (e.g., diffusion models) have become a leading way to encode the prior. Recent state-of-the-art diffusion solvers lift these priors to function spaces, finding a physics-consistent reconstruction in the output space of the diffusion denoiser. We prove that, in a discontinuous PDE setting, output space methods can result in failure to appropriately minimize the unobserved error with the correct coefficient field. Consequently, we propose Function space Backward-Consistent Sampling (FunBCS), an input space ...
| Authors | Yida Pan, Muhammad H. Ashiq, Chanyong Jung et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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