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We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary…

Normalizing flows model probability distributions through an expressive tractable density. They transform a simple base distribution, such as a Gaussian, through a sequence of invertible functions, which are referred to as layers. These…

In image restoration, single-step discriminative mappings often lack fine details via expectation learning, whereas generative paradigms suffer from inefficient multi-step sampling and noise-residual coupling. To address this dilemma, we…

We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive…

Rectified Flow offers a simple and effective approach to high-quality generative modeling by learning a velocity field. However, we identify a limitation in directly modeling the velocity with an unconstrained neural network: the learned…

Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…

Complex systems with many degrees of freedom are typically intractable, but some of their behaviors may admit simpler effective descriptions. The question of when such effective descriptions are possible remains open. The paradigmatic…

We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned…

Language models are prone to dataset biases, known as shortcuts and spurious correlations in data, which often result in performance drop on new data. We present a new debiasing framework called ``FairFlow'' that mitigates dataset biases by…

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…

Discrete flow-based models are a recently proposed class of generative models that learn invertible transformations for discrete random variables. Since they do not require data dequantization and maximize an exact likelihood objective,…

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending…

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored.…

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type…

Variational flows allow practitioners to learn complex continuous distributions, but approximating discrete distributions remains a challenge. Current methodologies typically embed the discrete target in a continuous space - usually via…

We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…

We define canonical refinements of Harder-Narasimhan filtrations and stratifications in moduli theory, generalising and relating work of Haiden-Katzarkov-Kontsevich-Pandit and Kirwan. More precisely, we define a canonical stratification on…

We prove long-time existence of the Ricci flow starting from complete manifolds with bounded curvature and scale-invariant integral curvature sufficiently pinched with respect to the inverse of its Sobolev constant. Moreover, if the…