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While diffusion models excel at generating high-quality samples, their latent variables typically lack semantic meaning and are not suitable for representation learning. Here, we propose InfoDiffusion, an algorithm that augments diffusion…

Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In…

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…

We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…

Optical micro-manipulation techniques has evolved into powerful tools to efficiently steer the motion of microscopical particles on periodic and quasi-periodic potentials, driven by the external electromagnetic field. Here, the dynamics of…

Diffusion models are a state-of-the-art generative modeling framework that transform noise to images via Langevin sampling, guided by the score, which is the gradient of the logarithm of the data distribution. Recent works have shown…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

We addressed the problem of detecting the change in behavior of information diffusion from a small amount of observation data, where the behavior changes were assumed to be effectively reflected in changes in the diffusion parameter value.…

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have…

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Exponentiated gradient descent (EGD), a biologically motivated optimisation algorithm that respects Dale's law, produces log-normally distributed synaptic weights at convergence, in alignment with experimental observations in neuroscience.…

We propose a method for sampling from Gibbs distributions of the form $\pi(x)\propto\exp(-U(x))$ by considering a family $(\pi^{t})_t$ of approximations of the target density which is such that $\pi^{t}$ exhibits favorable properties for…

Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…

By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…

Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…

In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a…

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of…

The replica exchange method is a powerful tool for overcoming slow relaxation in molecular simulations, but its efficiency depends strongly on the choice of the number and interval of replicas and their exchange probabilities. Here, we…