Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs). The method addresses three challenges in PDE-constrained inversion: implicit sample-based priors without tractable densities, high-dimensional spatially distributed parameters, and the high cost of repeated forward-model evaluations during posterior sampling. L-DPS combines a variational autoencoder, an unconditional latent diffusion model, diffusion posterior sampling, and a differentiable neural surrogate. The VAE maps the parameter field to a lower-dimensional latent space, the diffusion model learns an ...
| Authors | Yuanzhe Wang, Alexandre M. Tartakovsky |
|---|---|
| Primary category | cs.CE |
| Published | 25 June 2026 |
| Last updated at source | 25 June 2026 |
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