相关论文: Mean-field Chaos Diffusion Models

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential,…

We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit…

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

Score-based generative models (SGMs) need to approximate the scores $\nabla \log p_t$ of the intermediate distributions as well as the final distribution $p_T$ of the forward process. The theoretical underpinnings of the effects of these…

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and…

A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…

The perceptual-based grouping process produces a hierarchical and compositional image representation that helps both human and machine vision systems recognize heterogeneous visual concepts. Examples can be found in the classical…

In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…

Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key result in this area shows that with accurate score estimates, SGMs can efficiently generate samples…

Automatic modulation classification (AMC) is essential for wireless communication systems in both military and civilian applications. However, existing deep learning-based AMC methods often require large labeled signals and struggle with…

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…

Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond. They achieve state-of-the-art generation results in various generative tasks. A great diversity of conditioning inputs, such as text…

Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…

Conditional medical image generation plays an important role in many clinically relevant imaging tasks. However, existing methods still face a fundamental challenge in balancing inference efficiency, patient-specific fidelity, and…

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…

Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and…