Statistics Seminar - Mu Niu (University of Glasgow)
| Dates: | 18 November 2026 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Title: Learning Geometry from Data: An Intrinsic Diffusion Approach to Generative Modelling
Abstract: Many modern datasets, including images, remote sensing measurements, and biomedical data, are high-dimensional but often concentrate near lower-dimensional manifolds with complex non-Euclidean geometry. Ignoring this geometric structure can limit the effectiveness of statistical and machine learning methods, particularly in sparse-data settings. In this talk, I will present a data-driven framework for learning latent geometric structure from data and incorporating it into stochastic processes defined on learned manifolds. Within this framework, I will focus on diffusion-based generative modelling, where geometric information is used to guide the diffusion dynamics and improve generation in sparse-data settings. In particular, I will introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), which combines probabilistic dimensionality reduction with score-based diffusion on learned manifolds. ILDM employs a hybrid diffusion process that adaptively switches between Riemannian and Euclidean dynamics according to mapping uncertainty, allowing the model to exploit geometric information where it is reliable while retaining robustness elsewhere. Experiments on COIL-100, MNIST, and cardiac MRI datasets demonstrate substantial improvements in generation quality compared with standard diffusion and latent diffusion models. The talk highlights how latent geometry, stochastic processes, and diffusion models can be integrated to develop robust generative methods for complex data.
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Frank Adams 2
Alan Turing Building
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