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We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…

Diffusion models have seen immense success in modelling continuous data across a range of domains such as vision and audio. Despite the challenges of adapting diffusion models to discrete data, recent work explores their application to text…

In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

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 present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

The relaxation towards equilibrium of systems with long range interactions is not yet fully understood. As a step towards such a comprehension, we propose the study of the dynamical equilibrium fluctuations in a model system with long range…

Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…

Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

This paper considers the problem of designing time-dependent, real-time control policies for controllable nonlinear diffusion processes, with the goal of obtaining maximally-informative observations about parameters of interest. More…

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…

In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an…

The stochastic efficiency of effusion as a thermal engine is investigated within the framework of stochastic thermodynamics. Explicit results are obtained for the probability distribution of the efficiency both at finite times and in the…

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of…

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true…

In a preliminary attempt to address the problem of data scarcity in physics-based machine learning, we introduce a novel methodology for data generation in physics-based simulations. Our motivation is to overcome the limitations posed by…