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Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that…

This is an expository paper on the theory of gradient flows, and in particular of those PDEs which can be interpreted as gradient flows for the Wasserstein metric on the space of probability measures (a distance induced by optimal…

The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…

In response to global concerns regarding air quality and the environmental impact of greenhouse gas emissions, detecting and quantifying sources of emissions has become critical. To understand this impact and target mitigations effectively,…

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…

We consider the problem of designing constraint-aware flow matching (FM) models that address the issue of constraint violations commonly observed in vanilla generative models. We consider two scenarios, viz.: (a) when a differentiable…

Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up…

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time…

Various machine learning tasks, from generative modeling to domain adaptation, revolve around the concept of dataset transformation and manipulation. While various methods exist for transforming unlabeled datasets, principled methods to do…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

We study the problem of sampling from a probability distribution $\pi$ on $\rset^d$ which has a density \wrt\ the Lebesgue measure known up to a normalization factor $x \mapsto \rme^{-U(x)} / \int_{\rset^d} \rme^{-U(y)} \rmd y$. We analyze…

Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the…

We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…