arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
arXiv:2609.36527v1 Announce Type: new Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. D...
arXiv:2609.15702v1 Announce Type: new Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.
arXiv:2606.22346v2 Announce Type: replace-cross Abstract: Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduc...
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
SBNO (Schr"odinger Bridge Neural Operator) is an equation‑free framework that learns conditional operators for both forward and inverse PDE problems using paired data and a diffusion Schr"odinger bridge matching approach. It preserves empirical input‑solution pairing through a mask‑aware endpoint coupling and supports both task directions within a single model. At inference, SBNO generates deterministic reconstructions via a probability‑flow ODE, achieving comparable or superior accuracy on five PDE benchmarks with only 5% observations, while being at least 9.7× faster and using 4.3× less GPU memory than guided‑diffusion baselines.