Mathematical Institute

Mon, 30 Nov 2026

14:00 - 15:00

Lecture Room 3

Physics-informed deep generative models: Applications to computational sensing

Professor Marcelo Pereyra

(Heriot-Watt University, Edinburgh)

Abstract

Professor Pereyra will talk about; 'Physics-informed deep generative models: Applications to computational sensing'

This talk introduces a novel mathematical and computational framework for constructing high-dimensional Bayesian inversion methods that leverage state-of-the-art generative denoising diffusion models as highly informative priors. A central innovation is the construction of physics-informed generative models using Langevin diffusion processes and Markov chain Monte Carlo (MCMC) sampling techniques to develop stochastic neural network architectures capable of near-exact sampling. The obtained networks are modular and composed of interpretable layers that are directly related to statistical image priors and data likelihoods derived from forward observation models. The layers encoding the data likelihood function are designed for flexibility, enabling scene and instrument model parameters to be specified at inference time and seamlessly integrated with pre-trained foundational generative priors. To achieve high computational efficiency, we employ adversarial model distillation, which yields excellent sampling performance with as few as four Markov chain Monte Carlo steps, even in problems exceeding one million dimensions. Our approach is validated through non-asymptotic convergence analysis and extensive numerical experiments in computational image and video restoration. We conclude by discussing unsupervised training strategies that allow the models to be fine-tuned directly from measurement data, thereby bypassing the need for clean reference data.

The talk is based on recent work in physics-informed generative AI for Bayesian imaging: https://arxiv.org/abs/2503.12615 (ICCV 2025), which uses a distilled latent Stable Diffusion XL model trained on five billion clean images as a zero-shot prior, and https://arxiv.org/pdf/2507.02686, which integrates pixel-based diffusion models with deep unfolding and diffusion distillation (TMLR 2025). The extension to video restoration is presented in https://arxiv.org/abs/2510.01339 (ICLR 2025). Our approach to unsupervised training of diffusion models is introduced in https://arxiv.org/abs/2510.11964.

Further Information

Biosketch:
Marcelo Pereyra is a Professor in Statistics and UKRI EPSRC Open Research Fellow at the School of Mathematical and Computer Sciences of Heriot-Watt University & Maxwell Institute for Mathematical Sciences. He leads pioneering research advancing the statistical foundations of quantitative and scientific imaging, shaping how image data are used as rigorous quantitative evidence, and forging deep connections between statistical, variational, and machine learning approaches to imaging. His leadership and contributions have been recognized through multiple prestigious awards, most recently a five-year fulltime EPSRC Open Fellowship to drive the next generation of breakthroughs in statistical imaging sciences based on physics-informed generative artificial intelligence. Prof. Pereyra will join Imperial College London in 2027 as Chair in Statistical Machine Learning in the Department of Mathematics.

Prof. Pereyra received the SIAM SIGEST Award in Imaging Sciences for his contributions to Bayesian imaging in 2022. He has held Invited Professor positions at Institut Henri Poincaré (Paris, 2019), Université Paris Cité (2022), Ecole Normale Superiéure Lyon (2023), Université Paris Cité (2024) and Centralle Lille (2025). He is also the recipient of a UKRI EPSRC Open Research Fellowship (2025), a Marie Curie Intra-European Fellowship for Career Development (2013), a Brunel Postdoctoral Research Fellowship in Statistics (2012), a Postdoctoral Research Fellowship from French Ministry of Defence (2012), and a Leopold Escande PhD Thesis award from the University of Toulouse (2012).

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