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We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient…
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…
Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…
Compositional score-based approaches to simulation-based inference (SBI) approximate the posterior over a shared parameter given $n$ independent observations by aggregating individually learned posterior scores: currently, there are two…
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation…
Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time. This process is issued from kinetic theory and is called Landau process, by analogy with the…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…