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Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…

An algorithm to estimate motion from satellite imagery is presented. Dense displacement fields are computed from time-separated images of of significant convective activity using a Bayesian formulation of the motion estimation problem.…

Diffusion models can be used as a motion planner by sampling from a distribution of possible futures. However, the samples may not satisfy hard constraints that exist only implicitly in the training data, e.g., avoiding falls or not…

The Diffusion Probabilistic Model (DPM) has emerged as a highly effective generative model in the field of computer vision. Its intermediate latent vectors offer rich semantic information, making it an attractive option for various…

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms…

This paper addresses the problem of optimal linear filtering in a network of local estimators, commonly referred to as distributed Kalman filtering (DKF). The DKF problem is formulated within a distributed optimization framework, where…

Diffusion Large Language Models (dLLMs) are rapidly emerging alongside autoregressive models as a powerful paradigm for complex reasoning, with reinforcement learning increasingly used for downstream alignment. Existing trajectory-based RL…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Decision-making stands as a pivotal component in the realm of autonomous vehicles (AVs), playing a crucial role in navigating the intricacies of autonomous driving. Amidst the evolving landscape of data-driven methodologies, enhancing…

Distillation addresses the slow sampling problem in diffusion models by creating models with smaller size or fewer steps that approximate the behavior of high-step teachers. In this work, we propose a reinforcement learning based…

Deep generative models are often used for human motion prediction as they are able to model multi-modal data distributions and characterize diverse human behavior. While much care has been taken into designing and learning deep generative…

We develop simple diffusion-advection models to estimate the average time it takes fish to reach one of the boundaries of an enclosure and the population distribution over time moving in the enclosure (such as a lake or slough). We start…

We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized…

Particle filtering (PF) is an often used method to estimate the states of dynamical systems. A major limitation of the standard PF method is that the dimensionality of the state space increases as the time proceeds and eventually may cause…

We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…

The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling…

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…