Related papers: Associative Memory and Generative Diffusion in the…

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…

Recently, large-scale diffusion models, e.g., Stable diffusion and DallE2, have shown remarkable results on image synthesis. On the other hand, large-scale cross-modal pre-trained models (e.g., CLIP, ALIGN, and FILIP) are competent for…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities for noisy versions of the data distribution at different…

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…

Constructing high-resolution 3D geological models from sparse 1D borehole and 2D surface data is a highly ill-posed inverse problem. Traditional heuristic and implicit modeling methods fundamentally fail to capture non-linear topological…

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…

Despite the remarkable generative capabilities of diffusion models, their integration into safety-critical or scientifically rigorous applications remains hindered by the need to ensure compliance with stringent physical, structural, and…

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…

Zero-shot learning enables models to generalise to unseen classes by leveraging semantic information, bridging the gap between training and testing sets with non-overlapping classes. While much research has focused on zero-shot learning in…

Diffusion models have emerged as a powerful class of generative models, achieving state-of-the-art results in continuous data domains such as image and video generation. Their core mechanism involves a forward diffusion process that…

We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…

Flat minima, known to enhance generalization and robustness in supervised learning, remain largely unexplored in generative models. In this work, we systematically investigate the role of loss surface flatness in generative models, both…

The evolutionary fitness landscape of biological molecules is extremely sparse and heterogeneous, with functional sequences forming isolated dense ``islands'' within a vast combinatorial space of largely non-functional variants. Protein…

Generative models can be categorized into two types: explicit generative models that define explicit density forms and allow exact likelihood inference, such as score-based diffusion models (SDMs) and normalizing flows; implicit generative…