相关论文: A Unification of Discrete, Gaussian, and Simplicia…

We construct a new class of infinite-dimensional diffusions taking values in a generalized Kingman simplex. Our model describes the temporal evolution of the relative frequencies of infinitely-many types which are "labeled" by an arbitrary…

Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or…

Generative AI has made impressive strides in enabling users to create diverse and realistic visual content such as images, videos, and audio. However, training generative models on large centralized datasets can pose challenges in terms of…

A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…

The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…

Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…

Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…

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…

Unmanned Aerial Vehicles (UAVs) are increasingly adopted in modern communication networks. However, challenges in decision-making and digital modeling continue to impede their rapid advancement. Reinforcement Learning (RL) algorithms face…

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in…

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for…

While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images…

The generative priors of pre-trained latent diffusion models (DMs) have demonstrated great potential to enhance the visual quality of image super-resolution (SR) results. However, the noise sampling process in DMs introduces randomness in…

The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional…

A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…

We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…

The integration of Differential Privacy (DP) with diffusion models (DMs) presents a promising yet challenging frontier, particularly due to the substantial memorization capabilities of DMs that pose significant privacy risks. Differential…

Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…

When models, e.g., for semantic segmentation, are applied to images that are vastly different from training data, the performance will drop significantly. Domain adaptation methods try to overcome this issue, but need samples from the…