相关论文: Monge-Amp\`ere Flow for Generative Modeling

Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine…

Previous work on controllable text generation has explored the idea of control from the latent space, such as optimizing a representation with attribute-related classifiers or sampling a representation from relevant discrete samples.…

We introduce TzK (pronounced "task"), a conditional probability flow-based model that exploits attributes (e.g., style, class membership, or other side information) in order to learn tight conditional prior around manifolds of the target…

Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or…

Data-carving methods perform selective inference by conditioning the distribution of data on the observed selection event. However, existing data-carving approaches typically require an analytically tractable characterization of the…

We investigate the approximation of the Monge problem (minimizing \int\_$\Omega$ |T (x) -- x| d$\mu$(x) among the vector-valued maps T with prescribed image measure T \# $\mu$) by adding a vanishing Dirichlet energy, namely $\epsilon$…

We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…

Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…

Flow-based generative models synthesize data by integrating a learned velocity field from a reference distribution to the target data distribution. Prior work has focused on endpoint metrics (e.g., fidelity, likelihood, perceptual quality)…

We develop an $\e$-regularity theory at the boundary for a general class of Monge-Amp\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\"older densities supported on $C^2$…

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…

In this work, we propose FlowTime, a generative model for probabilistic forecasting of multivariate timeseries data. Given historical measurements and optional future covariates, we formulate forecasting as sampling from a learned…

Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each…

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this…

We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…

We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for…

A gradient estimate for complex Monge-Amp\`ere equations which improves in some respects on known estimates is proved using the ABP maximum principle.

This paper provides a reinterpretation of the Drifting Model~\cite{deng2026generative} through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map…

In this work, we propose a novel generative learning paradigm, K-Flow, an algorithm that flows along the $K$-amplitude. Here, $k$ is a scaling parameter that organizes frequency bands (or projected coefficients), and amplitude describes the…