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Generative models for image generation are now commonly used for a wide variety of applications, ranging from guided image generation for entertainment to solving inverse problems. Nonetheless, training a generator is a non-trivial feat…

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time…

Recently, the rectified flow (RF) has emerged as the new state-of-the-art among flow-based diffusion models due to its high efficiency advantage in straight path sampling, especially with the amazing images generated by a series of RF…

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain…

We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success…

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…

This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…

Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…

Deep learning has revolutionized many industries by enabling models to automatically learn complex patterns from raw data, reducing dependence on manual feature engineering. However, deep learning algorithms are sensitive to input data, and…

Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing…

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Smart meter data is the foundation for planning and operating the distribution network. Unfortunately, such data are not always available due to privacy regulations. Meanwhile, the collected data may be corrupted due to sensor or…

Few-shot image classification remains challenging due to the scarcity of labeled training examples. Augmenting them with synthetic data has emerged as a promising way to alleviate this issue, but models trained on synthetic samples often…

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For…

The difficulty of obtaining paired data remains a major bottleneck for learning image restoration and enhancement models for real-world applications. Current strategies aim to synthesize realistic training data by modeling noise and…

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…

Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…

Data often are formed of multiple modalities, which jointly describe the observed phenomena. Modeling the joint distribution of multimodal data requires larger expressive power to capture high-level concepts and provide better data…

In recent years, generative models have shown remarkable capabilities across diverse fields, including images, videos, language, and decision-making. By applying powerful generative models such as flow-based models to reinforcement…