Related papers: Provable Mixed-Noise Learning with Flow-Matching

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the…

We study the convergence of the Expectation-Maximization (EM) algorithm for mixtures of linear regressions with an arbitrary number $k$ of components. We show that as long as signal-to-noise ratio (SNR) is $\tilde{\Omega}(k)$,…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…

Classical Mixtures of Experts (MoE) are Machine Learning models that involve partitioning the input space, with a separate "expert" model trained on each partition. Recently, MoE-based model architectures have become popular as a means to…

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Deep learning-based surface electromyography (sEMG) gesture recognition is frequently bottlenecked by data scarcity and limited subject diversity. While synthetic data generation via Generative Adversarial Networks (GANs) and diffusion…

Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…

Recent advances in inverse problem solving have increasingly adopted flow priors over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and…

Flow Matching (FM) has recently emerged as a leading approach for high-fidelity visual generation, offering a robust continuous-time alternative to ordinary differential equation (ODE) based models. However, despite their success, FM models…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems…

This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these…

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…

We consider the problem of single-channel audio source separation with the goal of reconstructing $K$ sources from their mixture. We address this ill-posed problem with FLOSS (FLOw matching for Source Separation), a constrained generation…

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…