Related papers: Hamiltonian Score Matching and Generative Flows

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite…

Traditional discriminative computer vision relies predominantly on static projections, mapping input features to outputs in a single computational step. Although efficient, this paradigm lacks the iterative refinement and robustness…

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…

In building artificial intelligence (AI) agents, referring to how brains function in real environments can accelerate development by reducing the design space. In this study, we propose a probabilistic generative model (PGM) for navigation…

We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining…

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…

Effective Hamiltonians arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, Hamiltonian dynamics, and Aubry--Mather theory. In Aubry--Mather theory, related objects, Mather measures,…

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible…

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…

Many score-based active learning methods have been successfully applied to graph-structured data, aiming to reduce the number of labels and achieve better performance of graph neural networks based on predefined score functions. However,…

Achieving chemical accuracy in quantum simulations is often constrained by the measurement bottleneck: estimating operators requires a large number of shots, which remains costly even on fault-tolerant devices and is further exacerbated on…

Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…

We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…

Diffusion models are routinely guided in practice by combining multiple score fields, yet the mathematical structure of score mixing is still poorly understood. We study the small-time generation dynamics driven by mixed scores $$…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

Given a compactly supported Hamiltonian diffeomorphism of the plane, one can define a generating function for it. In this paper, we show how generating functions retain information about the braid type of collections of fixed points of…

Diffusion model (DM)-based channel estimation, which generates channel samples via a posteriori sampling stepwise with denoising process, has shown potential in high-precision channel state information (CSI) acquisition. However, slow…

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…

Hierarchical Bayesian methods can unify many related tasks (e.g. k-shot classification, conditional and unconditional generation) as inference within a single generative model. However, when this generative model is expressed as a powerful…

The goal of this paper is to provide a new perspective on speech modeling by incorporating perceptual invariances such as amplitude scaling and temporal shifts. Conventional generative formulations often treat each dataset sample as a fixed…