Related papers: Degenerate diffusions arising from gene duplicatio…

Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that…

Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…

Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

Generative models have recently revolutionized image generation tasks across diverse domains, including galaxy image synthesis. This study investigates the statistical learning and consistency of three generative models: light-weight-gan (a…

This paper explores the challenges and benefits of a trainable destruction process in diffusion samplers -- diffusion-based generative models trained to sample an unnormalised density without access to data samples. Contrary to the majority…

Diffusion models are powerful generative models that achieve state-of-the-art performance in image synthesis. However, training them demands substantial amounts of data and computational resources. Continual learning would allow for…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Evolving genomes increase a number of their genes by gene duplications. To escape degradation in a functionless pseudogene, any gene duplicate needs to be guarded by negative (purifying) selection from otherwise inevitable fixation of…

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…

Diffusion-based models, such as the Stable Diffusion model, have revolutionized text-to-image synthesis with their ability to produce high-quality, high-resolution images. These advancements have prompted significant progress in image…

We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results…

Diffusion-based Deep Generative Models (DDGMs) offer state-of-the-art performance in generative modeling. Their main strength comes from their unique setup in which a model (the backward diffusion process) is trained to reverse the forward…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…