Related papers: On the Statistical Capacity of Deep Generative Mod…
Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion…
A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift \emph{along} the support of the data…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…
Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions…
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…
Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution…
Deep generative models open new avenues for simulating realistic genomic data while preserving privacy and addressing data accessibility constraints. While previous studies have primarily focused on generating gene expression or haplotype…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
Although deep neural networks are effective on supervised learning tasks, they have been shown to be brittle. They are prone to overfitting on their training distribution and are easily fooled by small adversarial perturbations. In this…
Simulation methods have always been instrumental in finance, and data-driven methods with minimal model specification, commonly referred to as generative models, have attracted increasing attention, especially after the success of deep…
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…
Generative Adversarial Networks have become a core technique in Machine Learning to generate unknown distributions from data samples. They have been used in a wide range of context without paying much attention to the possible theoretical…