Talks

(N.B. This page will be re-organised once the talk schedule is finalised)

Adrien Corenflos (University of Warwick) 

(Title: (TBC), Abstract: (TBC))

Francesca Romana Crucinio (Università degli Studi di Torino)

Title: Gradient Flows for Sampling: Why the Kullback–Leibler Divergence is Special

Abstract: Gradient flows have emerged as a unifying framework for sampling, optimization, and Bayesian inference. In the Wasserstein geometry of probability measures, the Fokker–Planck equation can be interpreted as the gradient flow of the Kullback–Leibler divergence, leading to a rich interplay between stochastic processes, optimal transport, and information theory. In this talk, I will introduce the gradient flow perspective on sampling and explain why the Kullback–Leibler divergence plays a unique role among statistical divergences. I will present recent theoretical results characterizing this uniqueness and discuss their implications for the design of sampling algorithms. Finally, I will highlight current developments beyond the classical Wasserstein setting, including Wasserstein–Fisher–Rao gradient flows, which combine transport and reaction dynamics to provide new perspectives on scalable inference and sampling.

Sam Duffield (Normal Computing)

Title: A Complete Decomposition of Stochastic Differential Equations 

Abstract: I show that any stochastic differential equation with prescribed time-dependent marginal distributions p(x,t) admits a decomposition into three components: a unique scalar field governing marginal evolution as well as a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field which can be chosen freely. I will discuss how the decomposition unifies previous work and describe some implications for MCMC and diffusion/flow generative models.

Karen Habermann (University of Warwick)

Title: Score matching for simulating sub-Riemannian diffusion bridge processes

Abstract: Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on Euclidean spaces, when considering diffusion processes on Riemannian manifolds the geometry brings in further complications. In even higher generality, advancing from Riemannian to sub-Riemannian geometries introduces hypoellipticity, and the possibility of finding appropriate explicit approximations for the score of the diffusion process is removed. We handle these challenges and construct a method for bridge simulation on sub-Riemannian manifolds by demonstrating how recent progress in machine learning can be modified to allow for training of score approximators on sub-Riemannian manifolds. Since gradients dependent on the horizontal distribution, we generalise the usual notion of denoising loss to work with non-holonomic frames using a stochastic Taylor expansion, and we demonstrate the resulting scheme explicitly on the Heisenberg group. Joint work with Erlend Grong (Bergen) and Stefan Sommer (Copenhagen). 

Lars Holdijk (University of Oxford)

(Title: (TBC), Abstract: (TBC))

Gurtej Kanwar (University of Edinburgh)

Title: Non-equilibrium sampling meets the renormalization group

Abstract: Lattice field theory plays a crucial role in systematic studies of strongly coupled systems across a variety of fields, including soft and condensed matter systems as well as fundamental particle physics. The key step in any lattice calculation is performing Monte Carlo sampling over the physical degrees of freedom, arranged in a regular grid in space or space-time. Unfortunately, state-of-the-art calculations face a rapidly growing computational cost as the resolution of the grid is made increasingly fine. I will discuss recent work using non-equilibrium and flow-based methods to resolve this slow-down by connecting to the renormalization group, which provides a coarse description of the same theory for low-cost, unbiased results.

Yvann Le Fay (CREST-ENSAE)

Title: On the complexity of standard and waste-free Sequential Monte Carlo Samplers

Abstract: We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of distributions, and then specialise our results to tempering sequences. We use our results to derive the complexity of SMC samplers with respect to the parameters of the problem, such as $T$, the number of target distributions, in the general case, or $d$, the dimension of the ambient space, in the tempering case. We use these bounds to derive practical recommendations for the implementation of SMC samplers for end users. 

Qing Li (Lily) (University of Edinburgh)

Title: Trans-Dimensional Sampling in State-Space Models and Multimodal Posterior Summarisation

Abstract: Many statistical models involve an unknown number of latent components, together with uncertainty over component-specific parameters and the allocation of observations to components. When these structures evolve over time, the posterior distribution is supported on spaces of varying dimension and may be highly multimodal, creating challenges for both posterior simulation and the interpretation of the resulting samples.   In this talk, I will consider a dynamic latent-component model motivated by multi-object tracking, in which component-specific parameters evolve according to state-space dynamics, while birth and death events change the model dimension. I will introduce a structured trans-dimensional Rao–Blackwellised Gibbs sampler that combines blocked Gibbs updates with an inner reversible-jump MCMC chain. The construction organises dimension-changing moves, continuous-parameter updates and discrete-allocation updates into tractable conditional blocks, while exploiting conditional Gaussian structure, parallel allocation updates and informed proposals. I will also discuss multimodal posterior summarisation for mixture and clustering models. Rather than reducing posterior draws to a single configuration, a Wasserstein-based compression represents the posterior by a small weighted collection of representative configurations, retaining multiple modes and providing an interpretable description of structural uncertainty. 

Song Liu (University of Bristol)

Title: Zero-Flow Encoders

Abstract: Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at t=0.5 if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. Online demo of our theorems can be found here.  

Samuel Livingstone (University College London)

Title: Scaling limits for adaptive MCMC

Abstract: (TBC)

Henry Moss (Lancaster University)

Title: Conditioning Gaussian Processes on Anything

Abstract: Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation -- including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.

Nikolas Nüsken (King's College London)

(Title: (TBC), Abstract: (TBC))

Marcelo Pereyra (Heriot-Watt University)

Title: Physics-grounded foundation models for generative Bayesian imaging 

Abstract: This talk presents a mathematical and computational framework for physics-grounded foundation models in Bayesian computational imaging, integrating physical forward models with state-of-the-art deep generative models such as distilled denoising diffusion models and flow maps. The resulting models are modular and interpretable, with layers that map directly onto statistical signal priors and data likelihoods. Likelihood layers are built for flexibility: forward model parameters can be specified at inference time, enabling zero-shot deployment with pre-trained generative priors, or fine-tuned for greater computational efficiency. The latter is achieved through consistency-model self-distillation, delivering strong generative performance in as few as three steps while retaining full forward-model flexibility and physical consistency. We validate the framework through extensive experiments in image and video restoration.  

The talk draws on a series of recent works in physics-grounded generative AI for Bayesian imaging: a zero-shot framework using a distilled latent Stable Diffusion XL model trained on five billion images (arXiv:2503.12615, ICCV 2025); its extension to generative video restoration (arXiv:2510.01339, ICLR 2026); a pixel-based approach integrating diffusion models with deep unfolding and diffusion distillation (arXiv:2507.02686, TMLR 2025); and a self-supervised framework for learning diffusion models directly from noisy and incomplete measurements (arXiv:2510.11964, ICML 2026).

Francisco Vargas (Xaira Therapeutics)

(Title: (TBC), Abstract: (TBC))

Darren Wilkinson (Durham University)

Title: Sampling approaches to Bayesian inference for discretely observed Markov processes

Abstract: Inferring the parameters of continuous-time Markov process models using discrete-time observations is an important practical problem in many fields of scientific research. Such models are very often "intractable", in the sense that the transition kernel of the process cannot be described in closed form and is difficult to approximate well. Nevertheless, it is often possible to (forward) simulate (approximate) realisations of trajectories of the process. There have been a number of approaches in the literature relevant to the parameter estimation problem, involving a mixture of approximate, sequential, and MCMC algorithms. This talk will discuss some of the different (simulation-based) inference approaches that have been proposed, paying attention to how well they scale with model complexity and are able to effectively exploit modern computing hardware such as GPUs. Emphasis will be placed on the problem of Bayesian parameter inference for the rate constants of stochastic biochemical network models, using noisy, partial high-resolution time course data. 

David Yallup (University of Cambridge)

Title: Phase transitions and nested sampling methods

Abstract: Many problems in the physical sciences exhibit critical phenomena around phase transitions, from lattice field theory to sampling molecular configurations. Particle methods provide a natural mechanism to approach these problems, providing an ensemble of information that can adapt to the target in question, however these targets are still a sharp challenge for Monte Carlo methods. In this talk I will review the nested sampling path, which contrasts favourably to tempering on problems featuring first order phase transitions, as well as the challenges this path faces both in practical implementation and theoretical grounding. Finally I will present a new formulation that extends the nested sampling path to a practical implementation with gradient based kernels, and demonstrate this with applications to problems in lattice field theory at scale.  

Rui-Yang Zhang (Lancaster University)

Title: Efficient and Exact Spatio-Temporal Posterior Sampling with VaSE

Abstract: Exact posterior sampling for spatio-temporal Gaussian process (GP) models is often computationally prohibitive, particularly over dense prediction grids. While state-space SPDE formulations reduce the computational complexity to linear-in-time, they remain cubic in the spatial dimension and become especially expensive when observation and prediction locations overlap only minimally. In this talk, I will present the Vanilla-SPDE Exchange (VaSE), a hybrid algorithm that exploits an exact equivalence between GP and SPDE formulations to enable efficient exact posterior sampling in this setting. I will demonstrate its computational gains through complexity analysis and numerical experiments. This talk is based on our recent paper: https://arxiv.org/abs/2606.31063.