相关论文: Steering Dynamical Regimes of Diffusion Models by …

Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…

Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…

Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…

As a generalization of deterministic, nonlinear conservative dynamical systems, a notion of {\em canonical conservative dynamics} with respect to a positive, differentiable stationary density $\rho(x)$ is introduced: $\dot{x}=j(x)$ in which…

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative…

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a time-indexed target path by reweighting…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…

Guiding unconditional diffusion models typically requires either retraining with conditional inputs or per-step gradient computations (e.g., classifier-based guidance), both of which incur substantial computational overhead. We present a…

We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…

We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein--Uhlenbeck process wherein the particle drift is modified by the empirical mean of its…

Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…

We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…

Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…

Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a…