Emile Mathieu

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

Protein design often begins with the knowledge of a desired function from a motif which motif-scaffolding aims to construct a functional protein around. Recently, generative models have achieved breakthrough success in designing scaffolds…

Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address…

Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…

Coupling normalizing flows allow for fast sampling and density evaluation, making them the tool of choice for probabilistic modeling of physical systems. However, the standard coupling architecture precludes endowing flows that operate on…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…

We introduce InstaAug, a method for automatically learning input-specific augmentations from data. Previous methods for learning augmentations have typically assumed independence between the original input and the transformation applied to…

The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success…

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…

Score-based generative models exhibit state of the art performance on density estimation and generative modeling tasks. These models typically assume that the data geometry is flat, yet recent extensions have been developed to synthesize…

We explain why directly changing the prior can be a surprisingly ineffective mechanism for incorporating inductive biases into VAEs, and introduce a simple and effective alternative approach: Intermediary Latent Space VAEs(InteL-VAEs).…

Learning representations of stochastic processes is an emerging problem in machine learning with applications from meta-learning to physical object models to time series. Typical methods rely on exact reconstruction of observations, but…

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…

We develop a generalisation of disentanglement in VAEs---decomposition of the latent representation---characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the…

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…