相关论文: Hamiltonian Score Matching and Generative Flows

Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

Diffusion generative modelling (DGM) based on stochastic differential equations (SDEs) with score matching has achieved unprecedented results in data generation. In this paper, we propose a novel fast high-quality generative modelling…

Guiding Vector Fields (GVFs) are a powerful tool for robotic path following. However, classical methods assume smooth, ordered curves and fail when paths are unordered, multi-branch, or generated by probabilistic models. We propose a…

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…

Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient…

Implicit generative modeling (IGM) aims to produce samples of synthetic data matching the characteristics of a target data distribution. Recent work (e.g. score-matching networks, diffusion models) has approached the IGM problem from the…

The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…

Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

We study the Hamiltonian flow for optimization (HF-opt), which simulates the Hamiltonian dynamics for some integration time and resets the velocity to $0$ to decrease the objective function; this is the optimization analogue of the…

Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…