Related papers: Learning Density Evolution from Snapshot Data

Most approaches to dense anomaly detection rely on generative modeling or on discriminative methods that train with negative data. We consider a recent hybrid method that optimizes the same shared representation according to cross-entropy…

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique.…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…

Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with…

The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…

We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long…

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…

Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…

This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…

We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…

Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…

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…

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…

We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional…

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing…

High-resolution rainfall observations are crucial for weather forecasting, water management, and hazard mitigation. Traditional operational measurements are often biased and low-resolution, limiting their ability to capture local rainfall.…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…

We consider the problem of learning a target probability distribution over a set of $N$ binary variables from the knowledge of the expectation values (with this target distribution) of $M$ observables, drawn uniformly at random. The space…

Various microphysical models attempt to explain the occurrence of broad droplet size distributions (DSD) in clouds through approximate representations of the stochastic droplet growth by condensation in a turbulent environment. This work…