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Spatially-explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density Surface Models (DSMs) are a two-stage approach for estimating spatially-varying…
We propose an efficient algorithm for learning mappings between two metric spaces, $\X$ and $\Y$. Our procedure is strongly Bayes-consistent whenever $\X$ and $\Y$ are topologically separable and $\Y$ is "bounded in expectation" (our term;…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…
To what extent can particulate random media be characterised using direct wave backscattering from a single receiver/source? Here, in a two dimensional setting, we show using a machine learning approach that both the particle radius and…
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures,…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of…
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…
Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due…
Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of LLaDA-8B-Base on masked…
The recently rising markup-to-image generation poses greater challenges as compared to natural image generation, due to its low tolerance for errors as well as the complex sequence and context correlations between markup and rendered image.…
We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local…
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
We consider the problem of identifying the signal shared between two one-dimensional target variables, in the presence of additional multivariate observations. Canonical Correlation Analysis (CCA)-based methods have traditionally been used…
Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the…