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Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…
Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify…
Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at…
Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…
We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, the known approaches to ascertain the existence of continuous Markov processes are based in the assumption…
Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…
We develop a flexible spline-based Bayesian hidden Markov model stochastic weather generator to statistically model daily precipitation over time by season at individual locations. The model naturally accounts for missing data (considered…
Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…
Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…