mlsanityData to 14 Oct 2026

Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEs

arXiv 2609.32941 ↗First posted 26 Sep 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

Inferring quantities of interest (QoI) from data is a central task in Science and Engineering. In such contexts, we often have access to both quantitative data and qualitative data. Quantitative data may be represented by noisy sensor measurements, simulation data, re-analysis data; qualitative data may be in the form of text descriptions of experimental setups, expected experiment outcomes, and human-perceived system behaviours. The task we address in this paper is the following. Given a training set of paired qualitative text and quantitative QoI data, we learn to exploit the inherent correlation between the two modalities to learn a highly informative data-driven natural-language-conditional Bayesian prior, such that when presented with a new physical system, we can coherently combine (i) the training dataset, (ii) qualitative text describing the new system, and (iii) a small number of noisy sensor readings from that new system, to perform inference and uncertainty quantification (UQ) over the QoI. To achieve this task, we develop two parallel approaches, one uses conditional diffusion and the other conditional autoencoders, and compare both against classical Bayesian methodology, unconditional generative models and deterministic supervised methods. Each approach has specific strengths and tradeoffs; conditional autoencoder offers theoretical tractability, allows for fast posterior sampling, and provides better-calibrated UQ, whereas conditional diffusion is explored for greater expressiveness and capturing complex posteriors with irregular QoI fields. The approach is tested on the steady-state heat equation, damped Helmholtz equation, and UK weather reanalysis data.

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References · 53

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  5. 2019Sentence-BERT: Sentence Embeddings using Siamese BERT-Networkscited by 9,170
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  7. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  8. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  9. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  10. 2022Generative Adversarial Networkscited by 5,627
  11. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  12. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
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  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  2. 2022Denoising Diffusion Restoration Modelscited by 963
  3. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 532
  4. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  5. 2018Pyro: Deep Universal Probabilistic Programmingcited by 380
  6. 2017Wasserstein Auto-Encoderscited by 373
  7. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 342
  8. 2017Compressed Sensing using Generative Modelscited by 339
  9. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  10. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Modelscited by 222
  11. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  12. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 152
  13. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 132
  14. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 127
  15. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 108
  16. 2023Score-based Data Assimilationcited by 96
  17. 2024Physics-Informed Diffusion Modelscited by 90
  18. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  19. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 68
  20. 2024On conditional diffusion models for PDE simulationscited by 60
  21. 2021Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learningcited by 57
  22. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 56
  23. 2020Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inferencecited by 42
  24. 2021Learning Functional Priors and Posteriors from Data and Physicscited by 37
  25. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 32
  26. 2021Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priorscited by 29
  27. 2024Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scalescited by 27
  28. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  29. 2021Prior knowledge elicitation: The past, present, and futurecited by 23
  30. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Priorcited by 17
  31. 2024AutoElicit: Using Large Language Models for Expert Prior Elicitation in Predictive Modellingcited by 15
  32. 2021Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learningcited by 14
  33. 2024Efficient Prior Calibration From Indirect Datacited by 11
  34. 2025A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptionscited by 10
  35. 2025LLM-Prior: A Framework for Knowledge-Driven Prior Elicitation and Aggregationcited by 6
  36. 2024Had enough of experts? Quantitative knowledge retrieval from large language modelscited by 4
  37. 2024A Primer on Variational Inference for Physics-Informed Deep Generative Modellingcited by 3
  38. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2

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