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Improving the reasoning capabilities of diffusion-based large language models (dLLMs) through reinforcement learning (RL) remains an open problem. The intractability of dLLMs likelihood function necessitates approximating the current, old,…

Functional connectivity (FC) refers to the investigation of interactions between brain regions to understand integration of neural activity in several regions. FC is often estimated using functional magnetic resonance images (fMRI). There…

The softmax activation function plays a crucial role in the success of large language models (LLMs), particularly in the self-attention mechanism of the widely adopted Transformer architecture. However, the underlying learning dynamics that…

Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based…

Large-scale training of latent diffusion models (LDMs) has enabled unprecedented quality in image generation. However, the key components of the best performing LDM training recipes are oftentimes not available to the research community,…

Deep Generative Models (DGMs), including Energy-Based Models (EBMs) and Score-based Generative Models (SGMs), have advanced high-fidelity data generation and complex continuous distribution approximation. However, their application in…

Speech super-resolution (SR) is the task that restores high-resolution speech from low-resolution input. Existing models employ simulated data and constrained experimental settings, which limit generalization to real-world SR. Predictive…

We present a discrete diffusion-based language model using Glauber dynamics from statistical physics. Our main insight is that instead of trying to train a discrete state space diffusion model using Glauber dynamics with a uniform…

Diffusion models have become a powerful family of deep generative models, with record-breaking performance in many applications. This paper first gives an overview and derivation of the basic theory of diffusion models, then reviews the…

Diffusion Probabilistic Models have demonstrated remarkable performance across a wide range of generative tasks. However, we have observed that these models often suffer from a Signal-to-Noise Ratio-timestep (SNR-t) bias. This bias refers…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent $q>0$, as well as its limit case $q=\infty$, which we refer to as the \emph{hard…

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…

Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and…

This paper focuses on establishing $L^2$ approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based on a decomposition theorem for convolutional kernels with a large spatial…

We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in…

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires…

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to $\textit{classify}$ between data samples and samples from some reference distribution. DRE-based models can…

There are two types of deep generative models: explicit and implicit. The former defines an explicit density form that allows likelihood inference; while the latter targets a flexible transformation from random noise to generated samples.…